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Yes Jayne is a Communist.

I am not sure if I actually need to deny such an obvious baseless slur, but for the record:
I spent some months living in Lithuania in the early 1990s shortly after it gained independence from the USSR.  (My husband is of Lithuanian descent.)  I personally witnessed the material and spiritual devastation left by Soviet rule.  I have had a strong visceral revulsion to Communism ever since then, in addition to the intellectual knowledge of its defects that any well-informed person would have.  It would be difficult to be more opposed to Communism than I am.

People nowadays are so used to "group think" that if one person in a movement has a differing view, then it clouds the entire group (this is just a communist tactic, based on emotion, which communists use to attack their opponents by pointing out "flaws" which aren't flaws but simply normal human disagreements in an organization.  On the contrary, when such disagreements arise in the communist party, they write it off as "his personal opinion".  Just another example of the double-standard which is inherent in communism and other deceitful movements).  

This just isn't logical.  If you were in the army and able to be a 'fly on the wall' of some of the high-level tactical meetings, you'd hear all sorts of disagreements and major confrontations.  But once the meeting is done, the General makes the decision and that's what the "rest of the army" hears - the General's decision.  You could also say that's how the Church works (or is supposed to).  Both the military and the Church are effective because of a hierarchy and an efficient structure.

In the case of the democratic process or a simple organization (especially volunteer ones), you'll never have the same level of hierarchy or obedience because the level of obedience required is lower than that of the military or the Church.  In the case of the Resistance, it's basically a volunteer organization of priests who decide to work together.  And, even if they took a vow to +Williamson, because the organization is in its infancy, the 'rules and regs' are probably minimal and not developed enough to address if or when a priest should comment on the topic of 'flat earth'.

So, if one priest in the Resistance speaks about 'flat earth', I say "who cares?"  Does this priest speak for the entire Resistance?  No.  Does he mean to speak for the entire Resistance?  No.  Does his opinion change the scope or purpose of the Resistance?  No.

So why does it matter what he thinks?  Why would the resistance be harmed?

I'm going to go ahead and let Pax Vobis speak for me here.
And then I'm going to lock the thread, since there's nothing more really to be said.
The solid answer is, "No, it wouldn't harm the Resistance as a whole even if he were pro-flat earth"
Priests each have individual opinions on everything -- everything that is open to opinion, that is. Now if you want to bring forward some actual heresy believed by this or that priest, I'd be happy to steer clear of that priest. Better get the word out.
But if your only complaint is "free speech! waaah!" then I'm not sympathetic at all. "In dubiis libertas".
And that category of dubiis (doubtful things) includes every secular topic there is, which the Church hasn't explicitly ruled on.

The "necessary things", on which we must have "unity", only include dogmas of the Faith and infallible pronouncements from the Popes. Now on debated points of theology, one shouldn't be completely rash (to dismiss a majority opinion, for example) but it still doesn't make one a heretic if you go with the minority opinion.

As for historical events, scientific matters -- go ahead and form whatever opinion you want. Popular or unpopular, likely or unlikely, you are completely free. It's not the concern of the Church.