When’s a right time for a 20 something college graduate to make their bank account independent of their parents?

(This is an opinion question, and Money.SE really frowns upon them, so I'm making it a Community answer. To be quite honest, this is a better question for InterpersonalSkills.SE.)

When’s a good time for someone working on their masters subsidized by their parents, and income from a job that doesn’t make too much money to break the joint bank account with their parents and have an independent bank account?

As soon as you got a job.

However...

subsidized by their parents

Would that emotionally hurt your parents? I metaphorically pushed my kids out the door when they graduated HS, but some parents are not only very clingy, but petty.

For example, yours might cut off support if you exert some independence.

Or... they might be clingy, and you might be afraid that they'd cut off support, but they wouldn't.

We don't know.

What you can do is open a new account, and slowly move all activity to that account.