An unlikely scenario, but I am interested to see what the thought pattern behind it is. If the opponent plays a Wildfire and both Maester Luwin and Bran are on the table, can I effectively keep 4 characters?

I assign the other 3 and then Bran is immune?

Since it is also a simultaneous effect I also assume that if I had more than 4 and didn't want to keep Maester Luwin, that I could still keep Bran?

Other than that, he can't be knelt by Filthy Accusations, but that is all that I can see off of that bonus.

Yes, Bran will not be killed by Wildfire while Maester Luwin is out - even if Bran is not one of the 3 you choose to live, and even if Wildfire kills Maester Luwin. This is because Bran is immune for the entire time Maester Luwin is in play, and all characters that are supposed to be killed by Wildfire would leave play at the same time.

Plot immune characters are also safe from Marched to the Wall (they can't even be chosen) and Power Behind the Throne (although "safe" is maybe not the best description).

Note that this question has come up often enough that it's in the unofficial FAQ , which points you to the following two threads explaining it in more detail.

I really appreciate that link and the responses.