Can one be paranoid and too trusting at the same time?

Too trusting means you are allowing someone more leeway than you should.
If you do that, and then worry and stress about it a lot, then yes, you are doing both.

Can’t you be paranoid regarding some things and trusting, even overly trusting, regarding other things?

Just because you are paranoid doesn’t mean that no one is out to get you.

A paranoid person can take measures to reduce their concern and anxiety and end up with a false sense of security.

Yes. You could be too trusting of some and too paranoid of others.

Ronald Reagan said “Trust but verify” which seems to be a combination of paranoia (or at least doubt) along with trust.