The Egyptian, who intends to change the club's name to Hull Tigers in time for the 2014-15 season, had earlier shunned the opportunity to consult fans and claimed he would refund their season tickets if they did not back the rebrand.
However, a spokesman for the leading campaign against the changes urged fans to remain patient and focus on the club's performances on the pitch.
"I think you can disagree with the name change while still supporting the team," Andy Dalton of the City Till We Die campaign group told Perform.
"There's no need to stay away just yet, anybody that does stay away, that's their decision to make, and people are becoming increasingly aggrieved by some statements that are coming out of the club.
"But there's definitely no reason to stay away at the moment. We can still support the team. They're doing very well and it's a pleasure to watch.
"We can do all those things while opposing the name change.
"Some people may feel that they don't wish to spend their money down there on a Saturday any more, but I think the majority understand that the name hasn't changed and I don't think it ever will to be completely honest."
And Dalton suggested that supporters did not necessarily disagree with Allam's ownership of the KC Stadium club, despite the ongoing dispute over its name.
"We're not even particularly opposed to the owner himself," he continued. "It's just one very strange idea he's got that we disagree with.
"I think people will continue supporting the team, while still stressing their opposition to overturning 109 years of history.
"We still want to very much focus on supporting Steve Bruce and the team. We want to do those things and, before the game, register the fact that we're not happy and that we want the club to go in a different direction.
"Ultimately, all we want is to put this nonsense behind us and 100 per cent support the team."
Dalton confirmed that the group would now consider asking the club to reconsider the decision not to consult the fans.
