No height standards that I ever heard of....can’t fit a 5’10 ft guy in a tank....as least not very well. Former 19k/19d then 09s/35d/35e here. 5’8”. (and I was a tall tanker)
Yes, I doubt they had height requirements in 1776. I'm sure they took anyone, of any height or even age, who was reasonably healthy, brought their own musket, and knew how to shoot it.
I also doubt they had a policy on gay troops in 1776. It probably never occurred to anyone that it was an issue. I'm sure there were some gay troops, but they kept their desires hidden rather than insist the Continental Army hold Pride! marches at Valley Forge.