There's no Michigan or federal law that protects lesbian, gay, bisexual, or transgender people from discrimination.
Michigan's civil rights law protects you from discrimination based on your religion, race, color, national origin, age, height, weight, familial status, or marital status.
Sexual orientation? No.
As Lester Graham has pointed out in the past:
It would be foolish to do, but Michigan business owners could put up a “Straights Only” sign in the window. It would be legal.
It's just something to keep in mind with all the outrage aimed at Indiana lawmakers and Gov. Mike Pence after the passage of the Indiana Religious Freedom Restoration Act. The Indiana law makes that type of discrimination legal explicitly.
Michigan and federal law just happen to be silent on that type of discrimination.