I think that it should only reset the rep to neutral if your rep with them is anything below neutral, cause I can only see it being useful to have in that situation.
But I was also wondering that let's say I wear faction armor, and I get some rep. If I were to be wearing that armor while gaining the rep, will could I be accepted whilst wearing it? If not, does the rep still enhance my "title"? (ie. Liked, Idolized, Troublemaker).