It's more typical for them to claim ownership of it, rather than to forbid it. Any job where you have to submit a list of prior work with your employment contract (which is most of them in my experience) is usually a sign that there's a clause in there claiming ownership of everything you do while employed there. Personally I doubt it's very enforceable, especially since California is so worker-friendly on everything else I know about, but I don't know how well these clauses work out in practice.
The stance on personal after-work projects, as well as whether or not you're to work in an open-space office, are two things I'd really love every job listing mentioned. It would be the primary filter for me.
California categorically prohibits this so all such provisions are null and void in CA.
Anything you develop during non-working hours, not at your employer's office, and on your own equipment is yours and employers are not legally allowed to have any claim on that work.