Tom Brady seems to be on the fence about showing respect for his country but also being united with his teammates against Trump -- so he's doing both ... and the Prez is down.

Tom was seen locking arms with a teammate Sunday during the National Anthem before his game against the Texans ... but he also had his right hand over his heart. 

The dynamic is interesting -- lots of NFL teams reacted during their Sunday games to Trump's comments about players kneeling and how owners and coaches should fire anyone doing it ... some knelt, some dodged, others linked up in solidarity. Tom chose the latter.

Here's the kicker ... Trump just commented on the arm locking, and he seems to prefer it as opposed to kneeling. The question -- did he do it just because Tom got involved?

The Patriots' fans, on the other hand, didn't take too kindly to the perceived protest of the National Anthem. 

Another installment in the Trump/Brady saga ... more to come, we're sure.