The law of chastity applies equally to heterosexuals and homosexuals alike. There are openly gay people who attend (and choose to attend) BYU but do not act on their attraction (break the law of chastity) and are fine.

I feel like this argument is largely based on a time before gay marriage was allowed.

At BYU, if I'm a straight male and have heterosexual sex outside of marriage, I'll be punished for it.
If I'm a gay male and have homosexual sex outside of marriage, I'll be punished for it.

So in that one point, no issues with hetero/homosexuality being treated the same.  But it misses much that IS different.

If I'm a straight male, I can kiss, go on a date with, or hold hands with a consenting adult to whom I'm attracted.
If I'm a gay male, kissing, dating or holding hands with someone to whom I'm attracted is a violation of the Honor Code.

At BYU, if I'm a straight male and marry (outside the temple, by civil authority), I can have as much sex (with my partner) as I want.
If I'm a gay male and marry (outside the temple, by civil authority), not only would sex within marriage be considered a deal-breaker, but so would the marriage itself.

It seems to me that there are clear differences in how the two are treated and what is allowable.  Arguing that they can do the same because everyone can date/kiss opposite-gender is similar to extremist Muslim theocratic governments arguing that everyone is equally allowed to practice the Muslim religion and that Christian faiths are equally barred for all residents, and that therefore there is no bias or discrimination.  After all, everyone is treated the same - nobody is allowed to practice aspects of non-Muslim religious traditions, whether you're Muslim or not.