He doesn’t have to appear unless they subpoena him. And then, even, he can challenge the validity of the subpoena before he shows his face before Nadler’s committee. At that time, Nadler will have to show his hand and if he’s on a fishing expedition he’ll have to say it. Of course, before a like minded judge, which they will make sure they get, Stone will probably lose, initially. But he can continue to keep fighting until it reaches SCOTUS, for all it matters.
And, if he’s forced to show up, then he can plead the 5th.
However, I’d love to see him show up and then start playing Candy Crush on his phone and not say a damn word.
While wearing a fishing hat.
Since he is currently in the middle of a criminal prosecution and the subject of the House’ testimony request is an area in which he is on trial for, ( or close enough to the trial issue), there is not a single judge that would order him to appear and answer questions.
First, making him appear and assert his fifth amendment rights would be seen as poisoning the jury pool, (which the gag order is supposed to be in effect to prevent), because of the optics of asserting the 5th in public.
Second, the judge in his trial would not allow it because it would set up a mis-trial situation or a major issue for appeal if convicted after having been forced to appear in the House committee.
Any witness in a congressional hearing can refuse to answer any question they wish. The committee would then have to convince the DOJ to prosecute him/her for contempt.
There are defenses for just such a scenario. A USSC decision in the 50’s concerning contempt of congress during the House Un-American Committee ruled that the questioning must be pertinent to the committee’s legislative duties, not a witch hunt and can not violate the witness’ 4th and 5th amendments.