The controversial Allam last week revealed he would either finally succeed in changing the club’s name to Hull Tigers, or sell the Premier League outfit based on "whichever came first".
Hull fans have made no secret of their views over his proposed name change, but Bruce wants them to back his new-look side against Sam Allardyce's men rather than stage another protest during the match.
"My appeal to all of the fans is that they can have their thoughts but once it gets to matchday, we need them to get behind the team," Hull manager Bruce said.
"We need them to do that because if it becomes fractious then it becomes difficult.
"When it becomes difficult then it can affect the team. That is why I appeal to the fans.
"We don't want any protests - even though I know nothing's changed on their behalf with the name-change issue.
"We want the supporters to get behind the team, that's my concern, and I'm sure they will.
"The protests hit their peak against Crystal Palace last season, and it seemed to wane after that. We lost that game and we should have won if I remember.
"We need all the supporters, if they can, to support the team. Of course they can keep their opinions - but not on a match day because that just harms everybody."
