Bf let family disrespect me

Could you be with someone who allowed their family members to disrespect you and didn't say anything to them about it? My bfs step sister sent me a foul message after me and my bf had an argument and when I brought it up to him (showed him the screenshot as well) he didn't seem to care and now I don't know how to feel.. I feel so disrespected and it hurts even more that he didn't stand up for me over something that was not any of her business. I don't even know the women like that as I've never spoken to her so it was even more of a shock to get a rude message from her. I immediately blocked her and that was that bc I'm a grown woman who doesn't have time for that immature bs. I've been with my bf over a year and I've never had to deal with something like this. Now I'm questioning our relationship bc if he can allow her to talk to me however she wants without saying anything to her does he allow his other family members and friends to do the same?

Just an fyi He told me later on that he was upset and that's why he didn't say anything to her but I just feel really hurt now and don't know what to do.. I told him it shouldn't matter how upset he was at me he shouldn't have allowed it If he loved me and had respect for me. Also she was there when we had the argument and it had nothing to do with her at all. We were outside and she came out of the house but he also admitted to talking to her about it.