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.

Please post a picture. Let's see if it's in regs or not...

I had a mustache for years while in the Service. I would get comments like it does not look professional (Frankly this is a BS response as there is not defined standard to what "Look Professional" means and is usually pulled out when they don't know what the reg really says) or "I don't Believe" MPs should have facial hair. I knew the regs and was soon left alone when I would not cower to bullying. Most people in the Army are going off what they "Grew up" with or what they were told they don't take the time to actually do the reading. I walk around now a days and just shake my head at all the uniform violations glad I'm retired because I would not have enough time in the day to walk from my office to the food court if I had to correct everyone of them.

Bottom Line know the reg. have it saved on your phone and be respectful when showing your CO is 8up.

Well you are in the Infantry and the 70's Porn stache look is big no-no these days. My COC used to come out and stare at facial hair looking for just one hair that went beyond the that pencil thin line above my lip or to to the left or right sectors of fire. I was always asked if I wanted to just shave it off or have my squad leader remove the offending hair with a tweezer. I shave it down to look like that whack job Gefreiter (lance corporal) in the Bavarian army during WW1 or Charlie Chaplan . That did not go over well, so in the best interest of making SP/4 I shaved it all off. Most regulations have some room for interpretation and you have to ask yourself do you want to be that guy of avid the spotlight. Being that guy is not good for promotion, detail selection or additional close supervision. Its really all about "Is it worth some facial hair to make life more difficult" When you become a CSM you can sport you facial hair, all gray like a champion.

That depends if you're realistically going to fight an article 15 for "failure to obey a lawful order" for something as trivial as a moustache. Pick your battles wisely.

If you are not properly grooming your facial hair he can have you shave it off.

No, But he might not be nice to you. I had the same issue with an 0-6. I was the only Staff Officer without my picture on the wall. But I was assigned, so I wasn't in his rating chain.

Don’t be that guy