The usual reasoning behind a crossbow ban is that the club has had problems in the past with crossbow shooters tearing up targets. Bolts bury up in the target butts and the shooters tear up the targets trying to dig them back out. That's especially true for clubs that use excelsior target butts. The obvious way around that is to have the crossbow guys bring their own targets from home, or maybe even get a bunch of 'em to band together, pool their resources and set up their own crossbow range. Maybe you should approach the club with that idea and see how it flies.
I belong to an all-traditional archery club and, even though I get to endure a bunch of razzing about it, they have accepted my change to crossbows pretty well. Of course, my having only taken one year off as an officer of the club in the past 15 years might have something to do with their acceptance.
But that raises another point. It's much easier for someone who is actively involved in the club to have an influence on the club's policies. The people who put in the effort to keep a club up and running really don't give a rip when someone starts whining about the rules when that someone is one of those who just shows up to shoot and never comes to meetings or lends a hand with the chores.