Should I be more compassionate or empathetic to my boyfriend's ex?

I'd really like to have some impartial advice on this situation with my boyfriend. Earlier on in the year I've had an encounter with his ex. In this encounter she called me claiming with him for the past 3 years, even living with him and other things. Basically to make me think I was the side chick. My boyfriend proved to me that she was lying and we moved on from it. Over the next few months the relationship really became rocky as my trust for him after her claims was really being challenged. The reason for that was because after she initially called me I saved her contact to my phone so I was able to see her whatsapp display pics and posts and you'll soon see that she did the same. At this time I had my display pic set with a pic of him and I. In response to this pic she would post pics with him(usually old pics of them or more so pics with him in the background) to make it seem like they were hanging out at the time(using captions). I knew that she was repeatedly lying because I was either talking to him or with him while she did. We have moved way past this now and the relationship is going well. However, it seemed/seems as though he was not very bothered by her actions and is even in contact with her at times. He says they don't speak often and aren't even really friends anymore as he keeps her at an "arm's length". I would prefer if he did not have contact with her at all because I would not condone anyone who made him feel the way she did me. He explained to me that she was there for him when he was in a very rough place and I know that he has been through a lot prior to meeting me, through which she supported him. So I can slightly understand why he would not want to be hard on her. He had her blocked on fb for a while but I recently noticed that is not the case anymore. Since then when we are hanging out there have been a couple of times that she's tried to call him which he did not answer. I just don't get why he hasn't set a boundary with her or why she just doesn't back off because she clearly knows he is in a relationship. The thing that I'm wondering though is if I should be a little bit more considerate of her pain about them not being together. I'm not sure why that is but he explained to me that she always wanted them to be together but I guess he was never fully interested in her. Then he met me and she's pretty much out the window. ( no they were not together when we met or at least not to my knowledge). But something that has me wondering if I should be more considerate of how she feels (because obviously she's not healed from whatever they went through or the rejection maybe) is that when we go out we take some really cute pics and he tends to worry about me posting a pic of us which will make her upset and cause a huge fall out for us again like it did previously when she went into this episode of trying to destroy our relationship. I just think she's psycho and don't really care if my posts upset her as this is my relationship and she needs to move on since it has nothing to do with her. I just don't get why he wants to protect her feelings so much either. Should I be more caring/considerate about how she may feel since she obviously needs to heal still?

What are you playing at saving her number? You walked right into her trap there because it gave her the perfect opportunity to taunt you and cause trouble. Delete and block her number so you don't see any of that crap. As for him still being in contact with her, that has to stop. Yeah she helped him with tough situations in his life, but all that is history now. She is his past. You are his present. He can't have both. If he is not bothered about her behavior like you said then ask him to cease all contact with her because it makes you uncomfortable and you want to move on from all that with him. Stress that you want to focus on your future together but can't do that with her in the background. If he loves you I'm sure he'll understand that.