As a child, I was in churches that required beards of church members (Amish and conservative Mennonite). I kind of see their point, although I would prefer to let people choose not to wear beards if they so choose. I also kind of see the point of regulating facial hair to a certain extent. At least, I understand their point of view better than the groups that don't allow beards.
The main thing that gets my goat(ee) on this topic is groups that actually forbid facial hair for men, or that require some high bar of personal conviction before they'll let you grow a beard. It's something that is so clearly a feature of the natural order for humans that I think you can argue they are seriously out of line in forbidding it. The groups that allow or require beards while forbidding mustaches are halfway there. I view it as something in the same category as 1 Tim. 4:3: "They forbid marriage and demand abstinence from foods that God created to be received with gratitude by those who believe and know the truth."
However, the topic of "to beard or not to beard" doesn't rank very high in important in my opinion. I might one day find myself a member of a church that allows beards but not mustaches, so that means the hair on my upper lip would have to go. I find that highly irritating, but not a hill worth dying on.