Most universities and colleges, even public ones, hold a copy right on their name, team mascots and logos, and thus have a legal right to regulate there uses.
While I see little logic to their denying the use of their name, in connection with your club, perhaps you can use the opportunity of having the club to educate them to the fact, that those involved in the shooting sports, are not the crazed paranoids so often stereotyped, by those opposed to firearms.
Many colleges shooting teams that compete nationally, check out the following link:
nrahq.org/compete/coldir.asp
Life is no joke but funny things happen
jon