Can my commander force me to shave my mustache because he doesn't like it, even if it fits the regs?

No. If you are in regs, then you are fine. I strongly suggest you know exactly what the regs are without a doubt in your mind, possibly have a print out with you. I see the other people who responded are just telling you to go with the flow, but that voids the regulation allowing you to. Keep in mind that they may try to get you on something else, but if you are doing the right thing at the right time, you'll be fine. I hate that people in charge retaliate with bullying when people dont do what the want based off of personal opinions, but it happens none the less.

Tldr: know the reg and keep it within Army guidance.

Trick question! No one's mustache can look professional and fit in the regs at the same time

If you are within regs you have that in your favor but like others have warned you need to be 100% sure you are within regs. I've seen a lot of folks try to fight this and realize they misinterpreted the grooming standard and that they were in the wrong. If a mustache is the hill you want to die on and you are within regs you can fight it but just be sure you are right and willing to go through this because it will get a lot of attention and not the good kind.