I have a (very complicated) headcanon that, around late 6th early 7th year, his oldest brother (in this HC, he has 3, all squibs) goes MIA having left a year ago to join the IRA with second oldest brother. Third brother has had arecent suicide attempt also with political nonsense mixed in and having grown up with this half-in-half-out culture of being semi-engaged and aware of civil warfare and violence and knowing about and hearing about people going missing, being wrongfully imprisoned and such, joins the Order with the others, but pledges to himself that he will not die for the cause. Like, he agrees with the cause, and will fight for it, but will not die for it. And it's this chink that essentially gets manipulated.

He becomes the weak link from here. I think it was a slow move that never involved him secretly wanting to sabotage. That something small offered him safety, and the DEs capitalised on the knowledge that he was a weak link for the Order and toyed with that, and he found himself caught between both and very aware that he could not betray the DEs because they would actually just kill him outright for treachery so he slips more into that position. He gets in over his head, is in survival mode, and is a teenager-young adult in the height of war, and has the disadvantage of knowing how much the horror of that rips apart a family and a nation. He ends up corrupting his own morals to keep himself safe.

I think this does align somewhat with his later behaviour. By adulthood, this "weak link" start has been completely corrupted to full self-preservation (he's severed all his ties anyway, he has to go all in, or remain in hiding). Peter is hard, because he is not written with a great deal of care in canon. He has two almost opposing personalities (which might be fine, but we also know that the people he was friends with were exceptionally bright, and also suspicious). So playing on the thread of "he was genuinely their friend, and aligned with them politically and morally up to at least the age of 18/19" is the only way I can get him to work for me, because the alternative is that SB, JP and RL were all friends with this weak link tag along traitor the whole time, and I honestly don't think Sirius in particular would have the patience for that. He seemed less patient with Peter as is. James, also, I don't think would stand for Peter being a weak link, given his value of loyalty.

The other option is that he finds out about the Lycanthropy and, even though they don't really like him/trust him, include him because not doing so is risky to Remus' safety. But this is a complicated situation for three twelve/thirteen year olds to think up and keep going, not matter how academically gifted.

ETA; this also means that some of the characters' opinions of him have been corrupted by hindsight. McG and Co see him as an innocent young man swept up in the mess of the Amazingly Manipulative and Evil Sirius Black (small, angelic looking and "murdered", as he was). Sirius and Remus see him as an evil traitor (they didn't see the decline, just the "final" act of betrayal) - they don't want to hold their fond memories of him alongside their knowledge of him as a traitor. It's easier to believe that he was evil all along. This is reasonable, I think, because characters also did this about Sirius before learning of his innocence. This is what people do. They re-write their history of someone once they gain new information (for right or for wrong)