Superhero Relocation Act while making public acts of heroism illegal, not in any way or form prosecute actual supers or infringe on their basic rights, unless you somehow consider super heroism as their inherited right. While Doom used our indifference toward SRA as opportunity for PR attack, concentrating on it means bringing our fight to chosen by him diplomatic battlefield, and spending actions on it, while we have much more promising angles of dealing with him on intrigue front.
I would agree with this, if it were not for Shego. I actually kinda suspect the original attack wasn't really on our PR. That's a side benefit, but the real goal was Shego. Shego hates the SRA, and everyone knows this. Doom is currently in conflict with us, and in conflict with his mysterious enemy back home, he needs someone fighting us so we are distracted, and painting us as anti-SRA is a good way to induce conflict with Shego. (remember, until he took the spot, Shego was the most hated enemy,)
Now, we have an advantage there that he doesn't realize, which is goodwill from the gala. Which means Shego is going to be less conflict-y. Buuuuut, "less" isn't "none". Shego may sorta not-hate us, but like, if we are getting in the way of her passion project* she will likely fight us. As such, jumping onboard helps secure our border**.
Additionally, Shego is one of the few people with enough credentials as a super and a opponent that she could reasonably hijack the moment from Doom, so tying our star to her's isn't a bad idea.
*And Shego is nothing but passionate about spite
**Admittedly Dev is something of a problem in this calc, but I'd say we contact them turn after and make it clear we are pro-SRA due to political concerns over hardcore ideology, and she's likely to focus on Doom/Shego, understanding us as someone who will swap back if not pushed.