Should I feel bad for applying to two postdoc positions?
Everyone who is hiring knows that applicants are applying for multiple positions. This covers everyone from McDonald's to Harvard. It's expected. They will get multiple applications and will only take one, so you must apply to multiple positions to have a chance of landing one. Unless you have an offer in hand which you have already accepted when you apply for another position, you haven't done anything wrong. I'm surprised you've only applied to two.