Even for universities which have both MD and DO programs, you are still allowed to apply to AMCAS and AACOMAS (or TMDSAS if applicable). We have not seen any students put at a disadvantage to apply for both.
Applying to CASPA and AMCAS also does not put you at a disadvantage... although for some schools, medical school faculty can serve both admissions committees and may be put off by this. However, there are many more PA programs that stand alone and do not have MD faculty on their admissions committees.