Conor McGregor and the Paul brothers have apparently put their beef aside in the name of Donald Trump ... 'cause the trio of combat sports stars are currently chummin' it up at DT's inauguration!!!

The guys -- who've exchanged plenty of inflammatory remarks about each other over the years -- were all smiles as they headed toward Capitol Hill on Monday for The Donald's big afternoon in D.C.

McGregor actually sat next to Jake and Logan's mom while they were on their way to the festivities ... a sight that comedian Theo Vonn made a hilarious joke about.

The quartet then took a few pics together ... ones they actually shared on their social media pages just minutes ago.

"Inauguration going great," they said in a caption on the flicks.

Their fans raced to their comment sections to note the jovial nature coming from the guys -- as, after all, they've notoriously had bad blood for years. In fact, McGregor said just a couple weeks ago he'll be fighting Paul soon.

Of course, they've all been pretty staunch Trump supporters -- so it shouldn't be all that surprising they've put differences aside for a few hours.

Plenty of others in the sports world are slated to be in the building to help swear Trump into office ... Dana White and Joe Rogan are already there.

Jon Jones and Le'Veon Bell were seen making their way to the celebration earlier Monday too ... and numerous other athletes, we're sure, will be following suit shortly.