In America, the police have a reputation for being politically conservative. One rarely sees clashes between conservative demonstrators and police.
In Europe, though, there seem to be lots of clashes between anti-lockdown (presumably conservative) and (in France) yellow vests movement protestors and police? Is this because police in Western Europe skew left?
Speaking for Germany, officially they are bound to be neutral. Practically, they lean (heavily) right.
Looking at the anti-lockdown protests (which are indeed right to far-right), the police has been very hands-off compared to left-wing demonstrations.
In recent years, many cases of far-right extremist networks inside the police have been discovered (but as of yet no far-left networks).
The largest police union (GdP) is center-right, though even they see that many police officers are sympathetic to right-wing nationalism. The second-largest police union (DPolG) is hard right. There isn't any left-wing union.
Scientific analyses have shown that right-wing ideology is not an issue of a individual cases, but a structural problem in the police. Racial profiling is prevalent and right-wing extremism is under-estimated and institutional racism is negatively affecting police work (see e.g. NSU).
For France, the topic has covered been by a fact-checking article of a (left-leaning) newspaper, called Libération, published in 2018.
If you can read French, and if you know who the main figures of the different parties are, you could probably answer that police is most likely conservative there. (Note: blue is usually associated with the right wing parties, and red, with the left wing parties.)
Briefly, the article presents several surveys conducted by well-established agencies or labs, such as IFOP and Cevipof.
The method is quite direct: they asked policemen who they will vote for. The surveys include policemen, but also Gendarmerie, a similar but somewhat distinct force, as well as the military (not related to the question).
(militaires: military, policiers: police, gauche: left, centre: center, droite: right, ne sait pas: don't know)
(extrême gauche: far left, Hamon + Mélanchon: 2 heads of left wing parties, Macron: self-described as center, Fil[l]on + Dupont-Aignan: 2 heads of right wing parties, Le Pen: self-described as neither, but usually described as far right)
It seems obvious that armed forces (police, military, special services) attract more likely people who:
Being affiliated with weapons, having an autoritarian-leaning mindset and appreciating the current government are all conservative traits. Applicants for such services self-select to be conservative.
(Note that the self-labelling of a regime as "democratic", "socialist", "communist", or even "anarchist" does not change this analysis. You'll inevitably find that even the henchmen of truly revolutionary regimes will self-select this way, which is one of the problems with revolutions.)
Naturally, this pattern is not confined to Europe or any other region but applies there as well.
One mitigation strategy for the mitlitary is to have mandatory mitlitary service which restricts this self-selection to the officer grades. For example, Germany's problem with right-wing military factions has become more virulent since conscription ended together with the Cold War.
Not an easy question to answer, because it is hard to find unbiased reporting or studies on it.
@tim has given a good answer, I would like to add a different perspective:
When you check not the media, whose main interest is the generation of headlines, but the extremist groups whose main interest is self-defense against the police, you find that both left and right consider the police their enemy. I don't think I need to detail what the Antifa thinks about cops. But I have as well seen pamphlets circulating in right-wing circles with advise on how to act when police arrest or question you, and I could re-print them with minimal changes and give them to Antifa activists and they'd think their people wrote those.
If both the left- and right-wing outliers consider the police to be on the other side, then it follows that the police is on neither extreme. Which stands to reason given that "the police" is a rather large force with many different people in it.
Looking at the political spectrum and what the terms stand for, it's clear that "law and order" are more naturally associated with the right, so it is no surprise that studies find policemen more right leaning. That does not necessarily translate to right-wing opinions on questions such as immigration, employee laws, economic principles, healthcare, etc. etc.
The clashes you see are most easily explained by viewing the police as the defenders of the status quo and the current politics of the country, no matter what that is. When left-wing activists protest for better social support, they will clash with the police. When right-wing activists protest against immigration, they will clash with the police. And when Corona-tired conspiracy theorists protest the lockdown, they will clash with the police. Heck, if lunatics were to protest against the government keeping aliens from Jupiter prisoner in their secret vaults, they would clash with the police - and that doesn't mean the police is pro-imprisoning-aliens.
Some comments expressed this but none of the answers did. So, let's add this as an asnswer:
The question isn't very clear on distinctions between "police as institution", "police as policemen" and "police as in police bosses/brass".
For example, police brass (bosses) have been notoriously more left wing in many locales, as a direct consequence of the fact that they are more often than not political animals (at best, working WITH politicians, at worst, APPOINTED BY politicians) - and governments in places with more police - meaning more urban centers - are far more left wing than average for pretty much any country. Adding to this is progressive institutional capture - if you don't publicly support left wing goals (DEI, other such narratives), you face the same community/institutional pressure from activists and government as other institutions such as large corporations and colleges.
As specific consequences (and examples to prove this), police bosses often denied facts that would lead to "inconvinient to left wing" conclusions/demands, such as crimes disproportionately committed by a "protected minority" - for example Birmingham grooming gangs, where everyone can see the evidence, but police bosses loudly protested there was no problem. Same with "police can't enter" areas in some cities - if you ask a ground policeman, you will get one answer, if you ask their ultimate police boss, you get the opposite.
Police in general - both individually and institutionally - have a goal of "maintaining the order". In other words, they want to reduce upset to order, especially crimes.
Which means that police reaction to left or right wing is very likely to be predicated NOT on their politics, but on their risk to "cause problems" - meaning their tactics as well as their numbers. If a 100-member far left group stages a quiet sit-in without disturbing anyone, they are far less of a police-view "problem" than 3-member right wing group dead set on causing actual violence, but also far less of a police-view problem than 100K sized center left group - simply because 100K sized protest is a likely source of problems, regardless of views professed.
This is so strong, that it even produced a movie/fiction trope, where a policeman insists that some "good" but "looks like trouble/causing wave" character leave town; or both fictional AND REAL police frowning on vigilantes.
Police officers (and really any individuals that serve to guard the state to some capacity such as soldiers, intelligence officers etc.) have two influences on their political leanings as a generalisation, they are more likely to be associated closely with the power structure of the state and they are more likely to take a tough on crime perspective.
Most Western governments (including Western European) generally lean conservative, and as such the power structures of these nations tend to lean conservative. When most of the commanding officers of a police force are providing orders that align with their conservative political view, then this will be reflected in the police force (fear from officers to go against accepted beliefs also comes into play here; few people want to raise their voice against the crowd).
This as well as the fact that "tough on crime" is generally a conservative approach means that the person (police officer) holding that view is more likely to be conservative. Crime is mostly conducted by disadvantaged or ill individuals, and as the only tool (generally) available to police is to punish criminals to deter them, it can be clear to see why this goes against a left-leaning approach.
One thing that interests me is in most Western nations when a strong left-leaning party comes to power the police (and army and intelligence agency) seem to often attempt to undermine said ruling party. I wonder if a left-leaning party were to be able to hold onto power for a generation in a Western nation, if police (and others) would eventually fall in line with the shifting power structures of the state and become more left-leaning?
As an example of this last point I have often remembered a shocking (from my perspective) story from Australia between the years of 1951 and 1975 or so. The centre-right party of the time in 1951 created ASIS (Australia's international intelligence agency) without informing anyone of its existence outside of this party's highest members. During this time ASIS spent a great deal of its resources creating smear campaigns against the centre-left party at the time and have been confirmed to have been involved with the secretive disappearances and arrests of left-leaning public individuals. The centre-left party only eventually found out about ASIS in 1975 (about four years after they came to power) and even after ASIS was publicly revealed to exist they still directed most of their resources to undermining the ruling party.
I always found this story interesting (and shocking) and a good reflection of all these factors I talk about.
