PSL protects it's members through numbers, not anonymity. As a PSL member you're expected to be willing to put your name on your politics and be public about party affiliation.

I believe the disagreement goes all the way back to the Mensheviks and Bolsheviks - the Mensheviks wanted to allow members to the Communist Party to remain anonymous, such as a professor who might lose his position if he "came out" as a Communist. The Bolsheviks said: too bad, we all make sacrifices.

The PSL only makes two exceptions, as far as I'm aware: immigrants who are at risk of deportation may disguise their identity. And union leadership (and similar positions) are allowed to remain anonymous and this isn't too hard since those sorts of PSL members aren't really doing so much of the day-to-day work of organizing protests and other events.

I think this is a good system. It filters out people who are likely to get spooked on the job anyways. I think it's a matter of practicality. You have to give your home address to the council to speak at City and County Council meetings. You have to give your home address to run for public office (if you ever run into a petitioner for ballot access, they'll have a paper under the signature sheets that shows the home addresses of the candidates, and the legal names of their electors, and you have a right to see it if you ask). If you're registered to vote (and if you're in PSL, you're going to register to vote, and vote for the Party's candidates), literally anyone can Google your name and find your home address, because those are public records.