Trump has described Mexicans as "criminals" and said he wants to build a wall along the US-Mexico border.
The match will be played in Ohio, a key 'swing' state won by Trump.
Bradley said fans at the game must be respected, be they "American, Mexican, neutral, men, women, children".
Mexican President Enrique Pena Nieto has previously accused Trump of damaging US-Mexico relations, after the president-elect called undocumented Mexican migrants to the US "criminals" and "rapists".
He also said Mexico would foot the bill for his planned wall along the southern border of the US - a claim denied by the Mexican government.
"Given the way everything has gone the last few months, I think there is an added layer to this game," said Bradley.
"I would hope that our fans do what they always do, which is support our team in the best, most passionate way possible."
US goalkeeper Tim Howard said he hoped the game in Ohio's capital, Columbus, did not become overshadowed.
"That's politics, and this is football," said the former Manchester United and Everton player.
"Mexico is going to try to kick our asses and we're going to try to kick theirs. It's got nothing to do with politics."
Friday marks the start of the final stage of the Concacaf World Cup qualifiers, with six teams - the US, Mexico, Costa Rica, Trinidad & Tobago, Honduras and Panama - vying for three automatic spots at Russia 2018.
Donald Trump's victory in the United States presidential election has given an "added layer" to Friday's World Cup qualifier against Mexico, says USA captain Michael Bradley.