Sources connected to the Disney-owned network tell TMZ ... there has been no pressure to keep them off camera to avoid controversy. It's a particularly sensitive time, with Trump's latest attacks which have a huge swath of the country calling him racist. The UFC community -- both fans and fighters -- is diverse, and the presence of the Trumps is a powder keg.

Nevertheless, we're told UFC honcho Dana White is calling the shots on who gets on TV, and we're told the Trump kids will get as much air time as other big celebs at the Prudential Center in Newark. Not to say Dana's directing, but he gives broad directives, and there is no Trump ban.

Now ... we're told the commentators have been told ... NO POLITICS -- and that's squarely in line with ESPN's directive.

Eric and Donald Jr., along with his GF, Kimberly Guilfoyle, were invited to the fight by Colby Covington, who's headlining the main event against Robbie Lawler. Covington is a staunch Trump supporter who's rarely seen without his MAGA hat. POTUS even invited him to the Oval.

And, Dana himself is a die-hard Trump supporter, who even spoke at the RNC. Dana has famously said he will NEVER say anything bad about Trump, who was one of his first and biggest supporters in the early days of the UFC.