It has absolutely no negative impact on combat performance. If anything, the Sikhs have a renowned and respected record of being tough and courageous warriors. When Sikhs were in the military, they always weight toward combat arms.
So, yes, the prohibition is rooted in dogmatic ignorance.
So you want beards and nonmilitary headdress in the American military, that is your opinion, you side with the activists, that is fine.
I would like to see your proof of your factual claims though, I would like to see the unusual percentages of Sikhs towards combat arms and their reputation in the American military as being superior to Christian and atheist and Jewish soldiers.
We uncivilized north americans have a lot to learn from enlightened asians.