I'm a big fan of Holostars and I wanna throw my two cents in here.
I personally, would like to see more Hololive/Holostars collabs. Stuff like an Holostars meme review would be hilarious, Bar Robel/Holotalk with Kiara and Roberu, Astel and Ame playing Apex, Mori doing a song with Izuru and/or Astel, Ina drawing with Miyabi where they draw Hanasaki Forest animals sounds like a lot of fun, Astel and Towa playing Apex, Suisei/AZKi/Sora singing with Rikka/Izuru/Astel, etc. There's a whole bunch of stuff that I think would be really fun to watch, and I'm sure they'd all make it entertaining, and there would be a good number of people who would really enjoy these streams and would want more of them.
However, I don't want these things to be forced in anyway. If any of the Hololive/Holostars members don't want to collab with each other for whatever reason, they don't have too, and if you're a fan of either one of these branches, or both, you should respect their decisions. My life is not over because these collabs I personally would really love to see never come to pass. It's entertainment at the end of the day, and it feels self-serving to want to force your will onto these people when they may not want too.
I would also personally like it if even if they never do end up collabing, that fans should at the very least not get upset with them interacting with each other. Interacting with your coworkers shouldn't be seen in a negative way, that to me is a bit extreme, getting blowback from even interacting with someone on Twitter is a bit much and I hope that stops as soon as possible.
The last thing, and this isn't even necessarily my argument, but things I've seen people bring up and I personally agree with, which I'm paraphrasing a bit. They don't actually need to collab with any of the girls to succeed and do well. Yeah it helps, and there's been big subscriber jumps when they do, take Astel for example, but they still put a lot of effort in and have the talent to retain an audience and have people enjoy what they do. I'm not the kind of person who likes to compare numbers, but almost all of the Holostars soon are going to hit the 100k mark, and I think that more then enough qualifies them as a legitimate branch of the company, not that they weren't already. Even recently, there's been some cool sponsorships with cafes, Roberu recently got his 3D and a weekly radio show with Ono Yuuki I believe which is insane and I'm very happy for him, Rikka has been writing songs for anime, Izuru, Astel, and Aruran have been making rounds in the APEX Vtuber community, etc. They're doing well, and they're going to keep doing well. The other part that isn't my argument really is that there seems to be Holostars fans who want them to collab with each other for numbers reasons, which again seems very self-serving and the complete wrong way to go about the whole situation.
At some point, I think this stuff will change and more and more Holostars and Hololive collabs will happen, especially when newer gens come out in the future. I think people tend to worry about the talents more then they worry about themselves, and we should just enjoy the content we're getting and will get in the future. It's also possible that management knows about situations like this, and they might even be trying to figure out ways to get around it. These things take time to get over, but at some point, I think it'll be more commonplace. But again, don't force these things, let it happen naturally, and these kinds of negative situations could come undone.