Vigilante returns in Peacemaker Season 2, but unlike before, he doesn't seem as wild and out-there as he did previously, according to some fans. They feel that he appears a bit different, unlike before, when we saw much more of his playful banter with Chris Smith. He was also important to Chris' arc in the first season, where Chris was also dealing with his own father.
Adrian Chase and Chris go way back. They have known each other well since their years in school. Later, Chris becomes friends with Vigilante, deeming him just another hired gun by the forces. Unlike Chris, he doesn't think about the morality of his choices, which makes him all the more unhinged. He kills anyone and everyone simply because he has been told to.
Yet, that's not the only thing James Gunn's show revealed about his character. Behind his unhinged persona, Vigilante was also deeply in need of validation or human connection, even if he doesn't understand social cues like every other person. That made him a fun sidekick to Chris's morally conflicted antihero, trying to get his act together.
Unlike then, Peacemaker season 2 doesn't show much of Vigilante fighting alongside Peacemaker. So, fans speculate why it feels like he has lost his mojo.
Fans react to Vigilante being a bit off in Peacemaker Season 2

Vigilante entered the DC show as a masked anti-hero, forced to reveal his identity as Adrian. Since then, it showed him as a sociopathic but lovable anti-hero and a comic-relief character wrapped into one package.
He would poke you to ask him about some spider or bird facts, even if he didn't know anything about them. On the other hand, he would stand by Peacemaker's side and help him find a way out of any mess.
In Peacemaker Season 2, Freddie Stroma doesn't get as much screentime as he did before as Vigilante. Some fans believe it's because the show is more focused on establishing its multiverse-related subplot and the newer characters it has introduced this time. One fan (@Artemis-Rose-Eric) said something similar in a Reddit thread:
"Vig was my favorite in the first season. I guess they are rounding out some of the other characters for good reason. I justwant to see my unhinged boy do unhinged boy things with that sweet kindness he mixes into his violent behavior."

@thetiniestzucchini pointed out the change in Vigilante's arc in Peacemaker season 2, where he seems jealous of Leota Adebayo replacing him as Peacemaker's close friend:
"The arc for Vigilante this season is very clearly "I was Chris's only friend for a long time. Now I'm not. And I don't fucking like it, but I also don't know how to process it." So his "offness" and his absence plays into that. There are a handful of different ways it could play out where I'd be narratively satisfied, but I'm gonna be MAD if they drop the ball."

@OsirisReddit further pointed out two interesting theories about how Peacemaker season 2 might be building Vigilante for a much bigger purpose, to be revealed in the latter episodes:
" Two theories I have for Vigilante: 1: Adrian is the leader of the sons of liberty in the alternate universe and it’s given the obvious reveal that everyone is bad and that the sons of liberty were actually rebellions. 2: Alternate Universe Vigilante is pulling a Peacemaker on this earth, pretending to be earth prime Adrian in order to live his fantasy of being Peacemaker's best friend."

Peacemaker Season 2 is available to stream on HBO Max.
Also read: How did Chris hide the quantum folding chamber from ARGUS in Peacemaker Season 2? Details explored