What even is "Purity Politics", besides a phrase that's useful in thought-terminating cliches?
Some people play purity politics by judging the purity of the people who are being served. "Nope, you made bad choices, so you don't qualify for help."
And some people play purity politics by judging the purity of the people making the rules. "Nope, they want to do harmful things, so I won't vote for them."
And some people play purity politics by doing things in addition to (or even instead of) voting, because they judge the nation-state they live in to be an illegitimate government that could not do good even if it tried. "Nope, it's still in service to property and capital, I don't want better trained cops with more funding, I want community-based restorative systems of justice."
And yet... "You gotta vote for Our Candidate, the one I support despite every bad thing I've ever heard-and-ignored about them. What do you mean you won't vote for them, just like you and others warned everyone for the past two years before the primaries ever came up that you wouldn't ever vote for them for well-explained reasons that I ignored or brushed off? Your Purity Politics is why we'll lose! You are to blame for all bad things from this point forward!"