At Leavenworth, there were 3 chapels on post. However, 1 of them was Catholic only. That is because in short, in the mid 1800's, the Catholic church had built them and agreed to gift them to the Army. St. Ignatius, if memory serves me correctly was overseen in the building of it by Mrs. Sherman. Unfortunately it burnt to the ground in 2001. The other chapel is protestant and Catholic only. Main chapel is every religion. Upon the loss of St. Ignatius, Leavenworth expanded the main chapel, and other religious branches were going to be included in the design.
We have attended mass at many on base chapels. All of the ones that we have attended had the ability due to moveable walls to hide each religion's specific symbol. I.E. a Catholic crucifix does not look like a Protestant cross. In a traditional Catholic Church you will see the Stations of the cross throughout the church and stained glass windows. Base chapels you will not see that accept for Friday night Novena during Lent, and after Novena it is taken down at the end of the night.. The Xmas tree does not go up until a few days prior to Xmas. It is about the only time you will see any sign of Christianity everyday in the chapel.
Additionally parishioners every yr. fill out a survey regarding attendance. The amount of services and times offered come down to demand. If there are more Protestants than any other religion there will be more services for their religion.
So yes, the way the chapels are designed at many bases/posts, they can and will switch out the symbols, literally in about 15 minutes. I think for Muslim, the chapel design with pews makes it more of a problem than anything else.
Finally as usnabgo08 stated, the chapels are considered non-denominational. Our DS is getting married on base next yr. They have been told that the wedding must take place at 2:30 by the base priest because that is the only time assigned by the wing for Catholic weddings on a Sat. The other religions also have their set time on Sat. They must be cleared out by 3:30, so the Protestants can have their wedding service before the Catholics come back in for 5 p.m. service. The Catholics have to clear out by 6:30, so the jewish ceremonies can occur. (Jewish weddings must occur after sunset).