The words "purity tests" sets off my liberal detector, because of accusations of "purity testing" being used

Outside of any liberal usage, you have to acknowledge the phenomenon of leftist purity testing, especially on Lemmy. It's part of what makes the ML spaces so unsavory.

defend Democratic party entryism and terrible DSA candidates from criticism.

I mean,

A socialist or anti-imperialist movement does not have to be morally correct for me to back them.

Even the terrible DSA candidates are DSA candidates, and so far as socialist movements go they have the absolute advantage of popularity right now. I'm really, really tired of publicly glazing Democrats because the general class consciousness is so low that slowing the bleeding is the best we can get electorally.

I would be absolutely chuffed if terrible DSA candidates displaced terrible DNC candidates, because at the very least it puts "Socialist" in the general public awareness, and lowers the barrier for decent DSA candidates. And the DSA is a better class of lesser evil overall. And the better the lesser evil, the more effective my dual power is going to be.

Which is to say, purity testing is a real problem, and you don't have to be a liberal to recognize that any proper leftist movement is going to need to engage the actual proletariat, and most of those guys are tribalistic dummies.