I don't see why you would have any issue selectively prohibiting one over the other.

The costs of doing the loans may be prohibitive if you don't already have significant equity built up.  

Cost prohibitive repairs found?

There are some States (California, Texas, Louisiana...) where some of these structures are prohibited or complicated by local law and custom. 

The property owner and any agent of the property owner shall be legally responsible for directly or indirectly allowing, permitting, causing, or failing to prohibit the occupancy of a dwelling unit by more than two unrelated persons."

Technically, there is no explicit rule prohibiting you from getting an owner occupied FHA loan right now.

bill=201520160SB1053Existing law generally prohibits housing discrimination with respect to various personal characteristics including source of income.

In the very near future, it is expected that the criminal eviction will be prohibited in all of Arkansas.  

Also, if your property has an HOA, then they will prohibit short-term.

In CA, you would have to buy separate insurance for earthquakes and it is prohibitively expensive.