Personally OP, I don't like PDA at all, has nothing to do with Poly, I am an affectionate person to those I love, but I can't stand kissing or holding hands in public. Not because I am embarrassed or shy, I just don't want to do it. I don't need to show the world I am in love, I don't think the world cares to see me smacking lips with someone either. It is a level of exhibitionism I am uncomfortable with and perhaps you are too?
Nothing wrong with it, just tell her you don't care for making a public spectacle of yourself.