Alex herself is just a normal human who goes toe to toe with aliens every day, so she will at least know where James is coming from, while J’onn will probably recognize that they won’t stop James from doing what he wants to do.
It’s interesting to note that it won’t be so predictable on who will be okay with Guardian and who won’t be.
If I had to guess, I would say Martian Manhunter and Alex will be supportive while Kara will be against it.
On Supergirl, different characters will have their own reactions, and some might be more supportive than others.