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Nothing about the term tankie does or should deny their right to live. Advocating for the deaths of people who disagree with you is profoundly against everything liberalism (the freedom-based guiding principle of what we’d call “the west”) stands for.
To the contrary, as a pretty standard liberal American I fully support their rights to advocate for whatever they wish. Since there is no realistic way to accurately and objectively determine what is or is not propaganda, I support their right to create that as well.
Regarding the utility of recognizing where propaganda comes from, it can occasionally be useful to know, as it tends to follow certain patterns based on the goals of whoever created it.
You very well might be able to, actually, though I’m not going to guarantee it. Regardless though, if the line is commonly parroted by a certain group, then the claims are not particularly wild, are they?
And yes, there are lots of very useful tips that can identify most propaganda based off of common traits. This is not foolproof though. Still very good to know, though.