
Azothath |
yes. Spells sometimes target creature Types and thus changing the type would affect what spells can target it. Changing creature Type was a major reason PF 'fixed' polymorphing thus lending credence to the concern. It brings a host of changes like movement, attacks, natural attacks, monster type or racial abilities like pounce, rake etc.
If you are homegaming to allow a somewhat frequent change I'd review the various polymorph spells.
Eidolons have various shapes but once a class chooses a form it stays that way. There are specific spells to affect eidolons, familiars, etc.
I'd suggest you post in Advice or Homebrew forums for implementation/design advice.

Trokarr |

The phantom steeds type changes to animal but it remains a phantom not an animal companion. It’s stat block changes from that of a normal phantom (including type and number of attacks) but remains fixed and progresses normally as a phantom (mostly) and doesn’t really change beyond that. The animal “form” it takes is mostly cosmetic. Most effects that would normally affect a phantom would probably affect a phantom steed as well. That’s the way I read it anyway.