The former cycling star has shared his two cents on the matter over the last few weeks repeatedly ... especially after filming an episode of his "The Forward" podcast with Caitlyn Jenner.

On the pod, he and Jenner spoke about trans women competing against biological females -- and the two appeared to share the opinion that there should be a separate category for the parties, due to what they believed was an unfair advantage of being born a male.

While filming "Stars on Mars," Armstrong made no attempts to distance himself from that stance ... telling Ronda Rousey he doesn't see why it'd be "unfair" to introduce a new category to the sports competition landscape to assuage the issues.

Quickly, however, Tinashe jumped in to confront him over the thought process.

"We just have to care about if you other-ise people," the "2-On" singer said on the new Fox show. "It's not good for their mental health."

When Armstrong asked her to expound, she added, "Like, kind of, like, exclude them from the same spaces and places that everyone else is."

Armstrong swore he wasn't trying to exclude anyone with his ideas ... saying, "I sound like a right-wing lunatic. I'm not. I'm the most liberal person -- but from a sporting perspective ..."

But, Tinashe wasn't having any of it ... later telling Fox cameras, "I definitely didn't think that he should be the spokesperson for that."

Adam Rippon -- an openly gay figure skater -- also chimed in on Armstrong's remarks ... making it clear he was not a fan of them either.

"That is so disheartening," he said.

Rippon further explained he believed Armstrong's words could shake up the whole dynamic of the show going forward.