Abolish mandatory donations
There is no reason that viable student groups cannot raise their own money, either from the community or from alumni who were active in the organization during their college careers.
In 1998, members of Indiana University Students for Life objected to a grant given to a student group advocating for abortion rights. Also in the 1990's, a group called Students Against Fee Excess objected to the university's decision to allow INPIRG to collect donations through the bursar system. Christian students have objected for many years to the university's subsidies of the "Miss Gay IU" event.
I was reminded of these controversies (and a few others) when the Herald-Times reported that IUSA has reversed its policy and will now give money to eligible religious organizations in the wake of a complaint by the Alliance Defense Fund. People complained about the decision in the comments and suggested that "satanists" apply for funding.
Of course, there is a simple solution. Do not give any money to any student groups.
There is no reason that viable student groups cannot raise their own money, either from the community or from alumni who were active in the organization during their college careers. In the case of Christian groups, this should be even easier. Campus parachurch organizations should be directing Christian students to a local church anyway, so there is no reason they should not be able to get some financial help from some of the numerous churches in Bloomington.
This way, no students are forced to fund an organization or event that is in conflict with their ideological or theological beliefs through the mandatory student activity fee. Student groups that are strong enough to fund themselves will do well, while those who are weaker will not be artificially propped up by forced donations.
The advantage for the university is that it can truly can remain neutral, and avoid any conflicts that necessarily come when picking and choosing between organizations competing for limited funds.