The weird thing is that the other Seven Stars don't totally reject the idea. Based on S2E19, the only reason why they don't totally fall in with McGillis is because of Rustal's broadcast. While they try to play coy with it, they do acknowledge that they intend to stay neutral in order to not totally disobey Bael's orders, so they do actually acknowledge Bael's authority to some degree.

And excellent example of the cowardice typically found in career politicians; "I'm with whatever side wins" lol

McGillis's claim to Bael is his ability to pilot it. The show is pretty clear that that is the sole requirement for the right to lead Gjallerhorn. Being a Seven Star of course helped but that wasn't an actual prerequisite.

I would imagine "rightful ownership" would weigh in to some degree, otherwise if they decided to do something with the suit that required a test pilot, then that test pilot would theoretically, temporarily claim control over the organization. What I meant by not having a legitimate claim to the Bael, I was getting at the fact that it was under the ownership of Rustal until McGillis raided the storage facility and stole it. IIRC, this was even the reasoning Rustal gave for denouncing McGillis' "claim to the throne."

Weirdly enough, the other Seven Stars never once bring up McGillis not being Iznario's son. The head of the Mars branch does later on, but given that much higher ranked Seven Stars members seemingly don't care, I'd assume that it's not actually as relevant a factor because Rustal had already revealed he was adopted.

That is fair, I guess I was mostly just recalling the fact that McGillis and Rustal treated it as a big deal that de-legitimized McGillis' position in the organization.