My ex partners' child was just 3 when I met him, his parents had separated only 2 months beforehand (I had been told it was 6 m). His mum was already living with another man when I met him.
TBH the kid didn't have a clue, he just took everything for granted and had clear that I was not his mum but dad's girlfriend and that his dad was his dad and the guy at his house was mummy's new partner. It was just natural. So I am not going to jump on the wagon that such behaviour is necessarily rejection towards your new man.
However, I would say that you need to back off a bit, keep seeing new man if you wish, but not with DD around (I know is difficult to pay babysitting, but, if you get your child in the routine of going to sleep at 7, you can have new man around for dinner, movies, whatever without the need of your child noticing).
I think that you need that space to find out if your child is behaving like this because she is finding it difficult to get to grips with her new life/situation, or she is used to have the whole of your attention, feels ignored, is tired, or bored, etc. That behaviour doesn't necessarily mean she is being brainwashed by your ex into hating your boyfriend.
My son doesn't like his dad (dad was very abusive), absolutely adores my ex partner and yet sometimes he was rude to him. Considering how well they used to get along, instead of assuming the rudeness was because the dad/no dad situation, I just dealt with it as a normal parent who has not split: I just told him that what he had done was rude and to apologise as no child of mine was going to go and insult other adults, much less so my invitees.
Having said that, I give my son some margin for error and ensure that if we are going out a part of the day is child oriented, and that we involve him in what we are doing so he feels "part of the group". We also do things he doesn't like, but everyone has their turn here. But, it is important to make sure your child doesn't feel ignored or pushed to the side, as important as not letting her think she is the one calling the shots.