Does the United States have the most diverse military?

If not at the top, we've got to be #2 behind Great Britain.

Assuming the U.S. military is a reflection of American Society, then Yes. The U.S. is the most diverse nation on the planet from any Objective measurement we can use. Keeping in mind we're the 3rd largest by geographic size (trailing behind Russia and Canada [just barely]) and population (trailing behind China and India, not even close).

When you look at the size of the US military, we are also 3rd (behind China and India), but this is misleading due to the per capita ratio and total GDP expenditure. When you add in population homogeneity, it can be argued that we are likely the most Heterogeneous (diverse) military around.

Anecdotally, I had a roommate that was from Iraq. Served with several folks from Mexico. Knew of at least one guy who served in the French Foreign Legion, before joining the Corps. That's not counting Puerto Ricans, Guamanians, and Samoans (who are all Americans).

I'm guessing we are near the top of the diversity list. According to USNews, "The U.S. accepted 1,183,500 permanent migrants in 2016, remaining the top country for immigration."...and many migrants choose to sign up to join the US military. I think it is one of the strengths of our military as we are exposed to a diversity of perspective and understanding on a variety of topics.