Perrin actually knows about Mon Mothma's anti-imperial activities.
I've watched Andor all the way through so many times I've lost count, and I've been thinking alot about Perin and whether or not he knows about Mon's "activities". Personally, I think he was more clued in than Mon realized, here's why.....
During the season 1, when Perrin reminds Mon about the dinner party later that evening, she's upset about being at the same table as her political opponents. Perrin reminds her about the seating chart but throws in the bit about how maybe "they will think twice" the next time they have to oppose Mon in the Senate.
There's a quote about how Perrin was an "Academy Firebrand" by a character in the series and I can't help but think that Perrin was maybe a bit more passionate about politics when he was younger. It seems to me that Mon wouldn't let herself get tied to somebody who truly supports the imperial war machine.
The scene in the Limo when Mon confronts Perrin about his gambling, he responds that "This is someone trying to get at you through me." I feel that this shows that he is fully aware of her politics at least and that he looks out for indirect political attacks against Mon, trying to protect her, similar to the dinner seating chart.
During the second season, the scene where Perrin and Mon are having breakfast after the first night of the wedding, Perrin mentions that Tay Coleman had to be helped out at the end of the night because he was so trashed. He even gets in what seems like a dig about Mon and Tay apparently having an old fling together, but Mon dismisses it as nonsense. This seems like Perrin is warning Mon that something is up with Tay. He may not know all the details, but he has to be aware that they have been spending a lot of time together, and Mon's response to being back in an affair would be telling to Perrin that this wasn't the issue.
FInally, after the wedding during the dance party (Niamos rocks forever) when Mon let's go and gets drunk, there's that shot of Perrin watching her dance for a second. It's a deep look in my opinion and honestly it could mean whatever the viewer wants, but I feel that it's a knowing look. This man knows his wife, they've known each other and been together since they were young.
In conclusion, I don't think that Perrin knew exactly what Mon's activities were, but he knew that she was actively undermining the Empire at a minimum. His role was to care for Leida and provide cover when he could. It's interesting that he ended up with Skulden's wife at the end....did he get caught up by the ISB? Did Perrin turn Skulden in, to save what was left of his family? I think Perrin truly loved Mon and if he found out what she was up to, he wouldn't confront her, he would just quietly support her from the shadows.
Tell me what you think!