One of my best teachers used to caution that what looks malicious may be adequately accounted for by something else.
I’m guessing that your MIL and the ex shared something important to them, while your husband was in basic training. Perhaps they leaned on each other while missing him. Maybe they were fearful about whether basic would lead to deployment. Maybe they found a willing ear in each other for their worries in a way that other people neither understood nor supported. I have no idea what. But the depth of their bond speaks to something more than the usual connection between a high school girl and the mom of her boyfriend. Something clicked between the two.
I’m going to guess that your MIL doesn’t think she can have a similar relationship with you. She may be right. You’ve even indicated that she may find you intimidating, just for who you are, not for anything you’ve done.
If that’s the case, it could be that there is no malice here. Instead, MIL is doing her best to preserve the closeness she has with the girl while still acknowledging you. It’s probably difficult to do. She may be doing her best to be tactful to you both by keeping each of you on separate social media sites.
You say you know your MIL also cares for you and treats you with kindness. But it may be that she knows that the two of you will never become close. This isn’t a matter of making one relationship a priority over the other. It’s not a competition. To her, she only has different types of relationships with you and with the girl. For that reason, there is no reason to be insecure.
I don’t think the girl is, in your words, “accountable”. She isn’t doing anything wrong to be accountable for. From what you said, she isn’t trying to get back involved with your husband. She is keeping away from your marriage. She is only maintaining a friendship with someone who is important to her.
Your MIL’s friendship with the ex may become problematic if there are times that you (and especially your husband) really want and need her presence and she chooses instead to be with the ex. There are celebrations and changes in a person’t life where people often want their parents to be there. Be proactive. If you foresee that kind of conflict, it may be helpful to talk to MIL about it when there isn’t a social conflict. That would mean acknowledging the importance (to her) of her relationship with the girl but respectfully asking that she reserve some special times for her to be your husband’s mom.
Your husband is taking his mother’s continued friendship with his high school flame very personally. From what you wrote, I don’t think that the relationship is intended as an insult to him or as a negative comment on his choice of you for a partner. Cutting his mother off looks to me like an over-reaction. The fact that he moved on from that relationship doesn’t mean his mother needs to as well. Loving the girl doesn’t mean that his mother doesn’t love you or that she doesn’t support your marriage.
I wish you well.