People in the military who don't believe in God already have a vast support system in the military. You can get non-religious advice from uncounted varieties of family support, financial support, etc. Yes, religious people can also get secular advice and support from those sources.
The chapel exists to support people who HAVE religious beliefs. If the non-religious want to get together and do something together on Sunday morning, they can meet at the Golf Course (if it is a US Air Force base), the Gym, or gather in a dorm common room and watch secular humanists preaching humanism on any secular show - and there are hundreds.
The question is not "Does the military have support systems for non-believers?", because they do. The question is if religious people can be given any support in their belief in God. And for 200+ years, the answer has been, "Of course!" Refusing that would be bias and discrimination against believers. During the last half of my career, I averaged nearly 6 months a year deployed. Since I worked 7 days/week, I often forgot it was Sunday, or would have been hard pressed to get free during services. But I should not have been forced to spend half my adult life in a totally secular environment.
Although I'm a Baptist, I'm not big on going up to strangers and saying, "Are you SAVVEEDDDD?" It is like when the pastor of the church I go to wanted to go door-to-door in the local neighborhood. At 8 AM. On Saturday. I told him someone knocking on my door at 8 AM Saturday had better start off with "Your house is on fire!" Anything less than that would get him thrown off the property!
If someone asks me a question, I should be free to respond. If asked about XYZ, I ought to be able to include my belief in God in response, if it is relevant. And when I deployed to a tent in Saudi Arabia - as I did more times than I counted - I should have been able to go to a religious service when my military duties did not conflict. The chaplain might be Lutheran or Catholic instead of Baptist. Oh well. I've known some wonderful Catholics, and some rotten Baptists.
In Afghanistan in 2007, finding a Catholic priest would have been a challenge. The military tried, but having a priest available everywhere someone might be dying wasn't possible. But as a retired old fat fart, it seems the current military is increasing hostile to anyone who is a Christian, cowed by atheists who attack every manifestation of religious belief.
I went to college in Utah. I wasn't Mormon, but I didn't expect my Mormon neighbors to give up their beliefs to humor me. I didn't see any value in trying to stamp out any Mormon influence. If I couldn't stand Mormons, I shouldn't have gone to college in Utah. And in return, FWIW, the Mormons always treated me decently. Well, one guy refused to rent to me because I was Baptist, and I once heard a woman explain why she kept her kids away from our house on Halloween by saying, "You just don't know what a Baptist might do!"
But other than that, I had 6 years of good experiences in Utah...