I was surprised to learn that Estonia, Czechia, Finland, Poland, Latvia and Lithuania banned Russian citizens from entering for tourism purposes. What are the practical reasons for doing so? Or was it primarily done as a symbolic gesture of no practical meaning?
It's probably not due to fear of Russian special agents entering those countries, as it would be quite easy for an FSB agent to bypass these restrictions.
As you can read in a related Q&A Zelensky did seemingly aks for this. So that could be one reason. Another reason discussed in answers there is that tourist visas may be seen by some as "luxury goods", so simply a way to sanction Russia[ns]. As one British (somewhat right wing) journalist put it
How much longer should Russians be able to frolic on European holidays? Estonia’s prime minister, Kaja Kallas, says “visiting Europe is a privilege, not a human right”.
And some Russians seemingly didn't think twice about Z-symbols on their vehicles, when travelling to neighboring countries.
Third, in some of those countries you've mentioned it seems the topic was becoming political football, internally, and several of those countries were going to have elections at about the same time frame.
I managed to find a poll on this, from Sep 2022. Reportedly around 70% of Finns then supported the move "to stop issuing tourist visas to Russians".
Even in countries that were less politically inclined to sanction Russia[ns] as such, like in Armenia, there were concerns that the large 2nd wave of Russians (mostly draft dodgers--arriving on whatever travel arrangements they can) would have some disturbing impact on the local socioeconomic balance, e.g. by driving up rents. A similar story plays out in Georgia:
Many Georgians direct their ire not at the Russians but rather toward their own government, which has maintained a laissez faire approach to the mass influx. The government’s policy has long been oriented toward a normalization of ties with Russia via trade and tourism. [...] Faced with such criticism, the authorities have been trying to play down the volume and the impact of the Russian arrivals. Political opposition figures, meanwhile, are doing the opposite.
According to some local polling firm, some 69% of Georgians support a re-introduction of visas for Russians.
Even The Economist which is usually pro-immigration, and ultimately argues that Russian draft dodgers should be welcomed to Europe, has commentary like
Among large European countries only Germany and France have so far indicated that they are willing to let [draft dodging] Russians in. To get there, however, most would have to cross borders with the Baltic states and Finland. These countries are a lot less keen.
They—and others—have reasonable excuses. Poland has already accommodated millions of Ukrainian refugees. Russia’s neighbours, including the tiny Baltic states, Estonia, Latvia and Lithuania, have bitter experience of being ruled from Moscow and remain under constant threat from Mr Putin, who claims a right to “protect” ethnic Russians in neighbouring states. Estonia and Latvia have substantial Russian-speaking minorities, so adding a large influx of young Russian men understandably makes them nervous. You can see why they refuse to open their borders—though they might consider letting draft-dodgers pass through en route to the rest of the EU.
I know you're technically asking just about tourists, but the issues have certainly become intermingled since the "partial" Russian mobilization of last fall. Here's a semi-funny story relating to that point, about a Russian who ultimately went to Germany, first by crossing into Kazahstan, and even though no visa is technically needed for that step:
"The Kazakh [border] official asked with a grin where we were going. We'd made up a story beforehand: we were going to the mountains to see the snow. The border guard started laughing and we laughed too," he said. [...] Then Ilya flew to Cologne, where he applied for asylum.
The point is to tie responsibility to privilege.
There is a disconnect in Russian society that one is not responsibile for the acts of the government. If you have no choice in who rules you, then you do not share accountability for its policies.
The EU members reject this mindset. In their mind, Russian citizens are ultimately responsible for the acts of their government, even if they do not have democratic means to select it. Every Russian who is vacationing in Europe while the war rages on in Ukraine should be protesting in Russia, and if they do not care, then Europe will force them to confront their civic responsibility by sending them back.
In short, the privilege of accessing the pleasures of democratic world is tied to the responsibility of upholding the basic principles of democratic world order.
