Does applying for financial aid really decrease my chances of getting into public universities?

Answered

First, I'm not sure if you're in California or not—this answer varies depending on whether you're in-state or out-of-state. In general, very few public schools are need-blind (while a lot of top private schools are), and that means that financial need will in some ways be taken into account in the admissions process. If you're in-state, that effect should not be very pronounced, because these schools have many many spots available for students in their home states that demonstrate financial need.

However, if you're out-of-state, then yes, this can be a big factor. And generally, out-of-state students should never expect significant financial aid from public schools—especially the UCs, which rarely give significant merit or need-based aid to top students (outside the Regents scholarships, which are extremely competitive). The vast majority of out-of-state students at Berkeley are going to be asked to pay near to full price. If you have significant financial need, your aid prospects will be much better at similar private universities that are a) need-blind and b) guarantee to meet full financial need with their packages. PrepScholar has a good list of those schools here: https://blog.prepscholar.com/need-blind-colleges-list, and there are many that would be just as good academically as Berkeley for a fraction (after aid) of the cost.