It actually is perfectly allowable for civilians to get on base. Our kids played sports when at Ft Campbell and Knox, and their schools were on post. Whether football, track, baseball/softball, golf, cross-country, whatever, the opposing teams and their fans were from all over the area and simply signed onto post.
You could right now.
So, a civilian priest who signs onto post is just fine. And chapels are not in restricted areas. It would be easy to attend a chapel on post.
Also, many folks have their individual access to a military installation: some are retired, some in national guard/reserve, some have connections to other programs run on post, some have jobs at px, commissary, education center.
Thanks again for that important clarification. You can be sure then, that there will be a show down. Thanks! Rita .)