If by "proselytizing", they're trying to keep chaplains from forcefully "Converting" non Christians to Christianity, or vice versa, then they're absolutely Right. And that goes for those of other religions, trying to forcefully "Convert Christians to their Faith.
That clearly violates the First Amendment, and should be Prohibited. Chaplains are their to serve the spiritual needs of the service people, and also to answer questions that non Christians have about Christianity.
It's like the issue of wearing a Patch, bearing symbols that come from the Crusades. Doing that makes the troops into Crusaders for a given Religions. . . In that case, Christianity.
That Isn't the purpose of the Military, and Shouldn't be.