And yet, Labour leader Jeremy Corbyn apparently got into a nasty tiff with the once and future Jean-Luc Picard after Jez and Sir Patrick both attended the same theatre performance recently - this all according to Stewart himself.
In an interview with The New European, Sir Patrick recalls how his attempt at self-deprecating humour somehow managed to offend the man who could someday become Prime Minister.
"He was talking to a group of my friends after a theatre performance and I wandered up to join them," he remembered. "Jeremy's eye caught mine and he said, 'Oh you're looking very well', and I made some light-hearted riposte along the lines of, 'You can't judge a book by its cover'.
"For some inexplicable reason, this annoyed him, and he shot back, 'You know, Patrick, you could just have said, 'Thank you' instead of making a joke out of it'.
"I couldn't understand how he could take offence at such an utterly innocuous remark, and no-one else could, and it made for rather an awkward silence. I just thought, 'Oh well, I tried', and, after a suitable interval, I discreetly headed off home."
Stewart admitted that the encounter amplified his growing doubts about Corbyn, leading this lifelong Labour supporter to "probably turn to the Green Party" in the next general election.
"I certainly agree with their positions on Brexit and climate change," he said. "To be perfectly honest, I find it difficult to understand what Labour really stands for or what it represents right now. It doesn't feel like my party any more.
"I am not a politician and I am not a strategist, but I have a suspicion Jeremy believes a disastrous Brexit would benefit him politically, and, in all the chaos and confusion that would occur after the policy is implemented – in either a hard or a soft way, I might add – he sees himself taking power. It seems to me to be just plain wrong to play with the country's future in this way.
"What Jeremy doesn't appear to understand is that it would be the easiest thing in the world to attack the government on Brexit and to oppose it at every turn and to tear apart their arguments and expose it for what it is. There is, after all, nothing that is more opposed to basic Labour values than Brexit and I think just about everyone except him can now see that."
Stewart said his personal beliefs very much fall in line with that of his Star Trek character Jean-Luc Picard, who he'll soon be portraying again in a CBS All Access series about the next phase of the Enterprise captain's life.
"My character Jean-Luc Picard always stood for equality, democracy, fairness, and he had no interest in materialism and he hated prejudice," he explained.
While Corbyn may have lost Stewart's vote, apparently the Labour leader may still at least have the support of EastEnders hard man Danny Dyer.
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