Besides the usual disclaimer that "the West is not a hive mind", this Q blurs together vastly different levels of opposition. E.g. I'm sure the majority of US citizens (but maybe not all) would rather not have lived under Salazar's Estado Novo (TLDR version: it was dictatorship that promoted Catholicism, to a point, still maintaining church-state separation) ... even though it was in NATO from the beginning. (There were perennial conflicts within NATO between a set of countries that wanted to
hold Salazar over a barrel for his undemocratic
rule and those--including
most USA administrations--who thought that approach would have been counterproductive.)
And likewise, many (more) US citizens would probably not want to live in Saudi Arabia, but they don't mind (that much) buying oil from it or even selling it weapons (although they're probably more split on the latter).
And likewise if you ask: "should the EU condition some aid on democracy or human rights?" you'd get substantially different answers than to, say, "should the EU member states' armies invade some country to bring it democracy". (If you want to read EU's points why it thinks it should "export democracy" (by some means like "democracy conditionality" or elections observers you can read the official blurb here. Their "why" points are a bit standard: democratic peace theory, generating wealth, inequality reduction. One somewhat obvious point from that EU doc as far applying this "export" in practice is that the EU cares more
about democracy in its neighborhood than farther afield. E.g. conditionality means much less
in practice when it comes to China or Vietnam than it comes to "its neighbors south the Mediterranean".)
Without making such distinctions between levels of promotion (or conversely levels of opposition to alternatives), it's impossible to make any further progress on discussing a matter like this.
I don't want to get your numbered subquestions much, because the 1st one is rather silly considering that China's government is singing praises to Marx, who was not an ancient Chinese philosopher. The 2nd is basically circling back to the main issue above, but it's throwing in the referendum business... You might want to ask that separately, but FYI none of the 4 PRC constitutions were adopted like that. As for the 99.5% referendum-approved Iranian one (which is what seems to motivate that given your subsequent comments)... why does that remind me of some dubious referendums in the European past?! Mind you, two of the 3 parties that supported it (as opposed to half-dozen that boycotted it) were
soon banned thereafter as well. Members of one of those [3] original supporting parties were even hanged en masse in the next decade. If I'm to draw some parallel here between some regimes criticized in the West, Iran has some features in common with other regimes criticized in the West, which I could frame (modifying a Stalin-related joke): it doesn't matter who votes, it matters who decides who can run in the elections. E.g. "in 2004, [the Council of Guardians] again rejected nearly a third of the 8200 candidates, including 88 incumbent Majles deputies" (that's more than a quarter of the seats.) That critical paper then says/concludes "Needless to say, this is not consistent with any reasonable definition of democracy."
(I know a lot less about jigra, which was added in an edit to the Q. A cursory search suggests that the defunct US-backed regime actually did try use such a format sometimes, so I'm not sure the West is really critical of that. Of course, the same kind of assembly now unreservedly backs up the Taliban. It depends who's in it and how pliable they are to the men with the guns, I guess. As far as I can tell, the same kind of assembly was used to rubber stamp the [autocratic though somewhat anti-communist] regime of Mohammed Daoud Khan in the [pre-Soviet-invasion] past. Daud Khan's regime apparently relied extensively on ethnopolitics, but not quite majoritarianism, since the Pashto he exclusively promoted in army and government are only like 40% of the population of Afghanistan nowadays.)
I see Roger's answer has already "schooled" you on the difference between liberal and electoral democracy. This however is a bit less relevant to our discussion since generally speaking "the west" is also "exporting" human rights as well trying to apply it themselves, which is on the liberal end/angle of democracy. For an exaggerated distinction between the two; see "tyranny of the majority", which one might gorily exemplify as the 51% voting to eat the 49% for dinner.
If you want a philosophical defense against the latter see Rawls' "veil of ignorance", which is more or less an elaboration on the "Golden Rule". Aside to the aside: there are actually some subtle defects to using just that rule for human rights, e.g. Rorty's "[self]-consistent Nazi" argument which is actually explored a bit by the protagonist in The Man in the High Castle (if you like novels more than dry philosophy), although the latter explores it from a combination of social environment/pressure and true beliefs, while Rorty's argument is just about the latter.