Back when I was a paramedic, I worked on a volunteer ambulance. We received no government funding what so ever. Every year we had a membership drive. Newspaper ads, and letters mailed to every household in our district. That was our one and only yearly fundraiser. It was cheap - IIRC, it was $35 for an individual or $50 for a family for unlimited treatment/transport. Those who chose not to become members were treated just the same when a call came in - we would respond, treat and transport. The question of membership never came up. After the fact, non-members were sent a bill whereas members were not.
I don't understand how people who know they are not paying any firefighting tax would expect NOT to receive a bill. Especially if you do like our ambulance did and send letter to each household advertising memberships and mentioned that non-members would be billed for services if they call you. Certainly don't let their house burn down in an emergency, but bill them after the fact, and pursue collections if they refuse to pay and that's what your department decides to do.
I did not get any compensation for being a paramedic (other than paid training), but that does not mean that there are no costs for a volunteer organization. I seem to remember paying a good $80,000 per ambulance (that was back in the 80's and doesn't include the supplies inside). I can't imagine what a fire truck would cost these days.