I dont know the specifics of him and Rhys not being close friends anymore (clearly they dont hate each other because both casually mentioned the other the past years in passing favourably), it may not be Alice related, but just life. but generally speaking celebrities are strongly adviced to avoid getting involved/seen with parties that are in an explosive public fight. Either because association to that person can give you trouble or to their case (this is why we dont see any well-known celeb supporting Alice in public since the TRO beyond generic messages, and it's telling because you just know that Alice certainly has pushed friends to publicly support her while Ioan is probably the opposite, she admitted herself to be mad at the friends that are Switzerland). Often you end up also supporting the one who turns up being the one in the wrong, so you would want to avoid that embarrassement (which thanks to being fooled by Alice and particulary her Lorraine interview some celebs have already managed)
Additionally there is always danger with Alice going after you if you show yourself with Ioan or supportive of him or something: this is a woman that wrote 7 letters to his employer. It's actually remarkable that people like Kate Ford and Selma Blair show themselves supportive of Bianca on IG. Or that Zen Freeman and his wife invited Ioan and Bianca to his birthday party. Or that Mark Burnett and Roma Downey invite them to stuff. Even if in the grand picture Alice is a drop in the ocean in terms of reach it's all some trouble you'd rather want to avoid.
Alice is insignificant to Mark Burnett and Roma Downey. She's a nobody. Twitter would troll her relentlessly because there's no reason for Alice to troll them for inviting him to things. They aren't on social media inserting themselves into their divorce.
Piers Morgan has skeletons. She's a nutcase and vindictive. As she's done with Ioan, she will lash out and even tell exaggerated truths or outright lies about Piers if he inserted himself into it. It's not worth it for him to get involved and have her drag him and his wife into it. If she did, though, he would come after her hard. And she's afraid of Piers anyway. He's also too powerful and can be as vicious and as mean as she is.
Matthew Rhys probably just moved on and is in a different season of his life. It can be hurtful when long friendships aren't the same, but it's happened to all of us. I'm sure Alice was a huge part of the drift in the beginning, but men's friendships are often different than women's. He has a famous partner, a kid, stepkids, lives in NYC, has had successful TV shows for the past decade keeping him busy. So I think it's just that he's busy and friendships often change. We've all experienced that. Once close friends become more distant, touch-base friends, and you try for a while to hang on to it but get tired of being the only one trying. I'm sure they keep in touch here and there, though. Actor Billy Baldwin talked about that recently on his wife's holy-roller youtube channel, how he treasures his longtime male friendships that go way back, but he feels like he's the only one reaching out all the time. He was hurt by it. I understood what he was saying.