Having a thick skin does not mean you sit back while others heap abuse and ridicule upon you. Like I pointed out earlier, GWB took that route. Rather than laying off him, they piled on even more. It's the classic lesson most of us learn in the schoolyard. If we allow bullies to taunt us, than everybody in the school will eventually taunt us.
I think Trump has an incredibly thick skin. I can't think of another presidential candidate who survived so much incoming flack during a campaign. Not only did Trump survive it and get elected, he did so with a smile on his face.
He could have simply said, "Well, there they go again". Or, "Celebrities know nothing of domestic or international issues. Their opinions are just that, opinions". Trump needs not go personal, as he does frequently. It is unseemly for the President. Again, he's the President partially because of his Tweets, just wish he would tone down the direct personal attacks. There is other phasing to counter.