As Wikipedia says: "Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools and by inmates in prisons."
One of these things is not like the others. Is running your professional software team like a paramilitary group or prison the only way you can get them to stop "bickering"? For people who are immature enough to bicker about any difference between individuals, when you enforce the standardization of one attribute, they just switch to something else.
I don't think that running a software team like a paramilitary group is the only way to stop bickering, but some elements of how paramilitary groups are managed are very attractive in this context, and seem to have worked where I saw them applied.
The employees of a lot of banks happen to wear suits, shirts and trousers, programmers included. I wouldn't discount the benefit of this purely because paramilitary organisations also happen to enforce a uniform.
http://www.lel.ed.ac.uk/~gpullum/passive_loathing.pdf esp 3 (25)