Well, he does have full immunity if he was speaking or appeared to have been speaking as a member of that political body or as one of its member.
The no trespass order is just that, an order. If it could be seen as encroaching on his immunity (and I think it does) then he would have an actionable cause to follow through with if he wanted to. You cannot take any action against him IMO.
One of the purposes of the state granting him immunity is so that he could speak just as he did...horrific speech or not.
If he was speaking just as a citizen, he still has limited immunity in respect to standard testimony immunity ~ he did not threaten anyone, hence immunity attaches.
And even if testimonial immunity is not considered ~ he still has 1st amendment freedom of speech. He made no threats, no cause to issue out a no trespass order.
The guy's an idiot for saying "he's sorry".