There's a big difference between the military and local public safety organizations.
If a soldier comes into contact with a member of the public who doesn't like the soldier's tattoos, there's nothing the member of the public can do about it that will affect the soldier's employment, the Army's budget, etc.
In the case of a local fire department, the member of the public can complain to the fire chief's boss (Mayor, Council, Board of Directors, or whomever), conduct a public campaign to cut the FD's budget, etc.
The other thing is that the military still screens out people with tattoos that are gang related, offensive, etc. Even the Marine Corps recently added a policy that restricts new visible tattoos. Some of their members had to go so far as to docement their existing tattoos photographically and file the photos with the USMC.
The Army tattoo policy is less restrictive, but still has many restrictions. Soldiers can't just ink up wherever they like.