I was wondering the same, but have no background in what chaplains are or are not allowed to do. I do know that it didn't SEEM to be prohibited, as chaplains of various faiths were very open about sharing their beliefs. It's certainly possible that there are restrictions around it, but if so, they were widely ignored in the 80s and 90s.
There has been a lot of controversy in the last 4 or 5 years. The Army (and probably all the services, but I'm not sure) has been trying to squelch the chaplains to keep what they say PC. The Pentagon has SJW's, just like the rest of the country.