Is my job allowed to cut my hours because I went to church on Sunday?

Generally, no, they could not do this: the law specifically prohibits harassing or discriminating against people in employment due to their religions, and further requires "reasonable accommodations" to religion and religious observances, such as allowing an employee to have time off for church and scheduling him/her for a different shift or different hours, is such are available. They are allowed to do some "reasonable" investigation to confirm that your reason for being out was legitimate--e.g. they can ask for some information or documentation from/about the church to confirm you are a congregant--but once they've done that, they can't discriminate against you, which includes not punishing you by cutting your hours for church attendence.
Like anything else, there are some narrow exceptions. If the Sunday shifts/hours you have to miss are critical ones for this business, then they don't have to accommodate you and can take action against you for missing them. For example: when I was in college, I worked at  beach club over summer break where most of the work was Saturday and Sunday (the weekends were the critical days). If I been observant at the time and had to miss part of Sunday for Church, they could have punished me by cutting my hours or even fired me, since for a seasonal job where weekends are critical, it would not be reasonable for me to miss Sunday. But barring situations like there, where the missed hours are provably critical, they cannot retaliate against you.