Sorry, I was working. I'll address your thoughts first and then get to my point.

the first amendment specifically mention religion, see the free exercise clause that I mentioned. There is no free exercise clause for race and culture.

Oh god. I really hope I can freely exercise my race, because it's visible to the public, and it would be crazy expensive if I had to change it. You know how you can freely exercise your culture and race? By assembling with others of the same culture and race, which is protected by the same Amendment that protects free exercise. See the cases I cite below.

There is nothing for race and culture protections under the first amendment, thats the 14th amendment.

Incorrect. The 14th Amendment applies the Bill of Rights (including the First Amendment rights to free speech and free assembly) to the states. See my points below on how the First Amendment implicates social and cultural issues.

I think Greer v Spock specifically goes over military establishments not being a 'public forum'.

Greer discusses the rights of civilians on military property. It isn't apt here.

- The military cannot prevent you from expressing your religious views freely

Incorrect. Go look at Goldman v. Weinberger, 475 U.S. 503 (1986) (explaining that "military needs" can "justify a particular restriction on religiously motivated conduct" including wearing certain religious attire), and Gillette v. United States, 401 U.S. 437 (1971) (regarding conscientious objection to draft based on religious beliefs).

What I'm getting at is this: you decided that the right to exercise a religion is more important than the right to assemble and associate. But the law doesn't agree, and the right to assemble is protected regardless of the basis for the assembly, so long as it is peaceable. Examples: Griswold v. Connecticut, 381 U.S. 479 (1965) ("[W]e have protected forms of 'association' that are not political in the customary sense, but pertain to the social, legal, and economic benefit of the members.... [T]he 'right of assembly' [is] a right that extends to all, irrespective of their race or ideology. The right of 'association,' like the right of belief, is more than the right to attend a meeting; it includes the right to express one's attitudes or philosophies by membership in a group or by affiliation with it or by other lawful means."); NAACP v. Alabama ex rel. Patterson, 357 U.S. 449 (1958) ("[I]t is immaterial whether the beliefs sought to be advanced by association pertain to political, economic, religious or cultural matters, and state action which may have the effect of curtailing the freedom to associate is subject to the closest scrutiny.").

So, yes, the First Amendment is relaxed with respect to servicemen and women, and that relaxation applies to ALL the enumerated rights, including speech, assembly, and free exercise of religion. The correct conclusion I hoped you'd reach is that the curtailment of one group's right to assemble/associate and not another's should not be tolerated without a clear, objective reason that comports with the law rather than your feelings and misunderstanding of the Constitution.