The Utah Fight Song, "I am a Utah man, sir..." was, as I understand it, composed by an early football coach, perhaps with the aid of his players, perhaps with the aid of some alcohol.
It is an authentic and iconic anthem, its words demean no one, and it has been lustily sung by men and women alike for more than a century. Yes, the language is somewhat dated. But fight songs are not legal documents. They are expressions of spirit, and there is no reason other than a dearth of imagination why "I am a Utah man ..." cannot be enjoyed equally at women's sports events.
In any case, if anyone thinks they can write a better fight song, by all means they should be welcome to try. But in the meantime, please do not replace "I am a Utah man" with the sappy "I am a Utah fan" or engage in any other censorship. The institution in question is, after all, supposed to be a university.