I don’t think the free rider problem applies for pure charitable donations, but I see now why you made the link with taxation.

You regard a donation to the Red Cross as a contribution for services that you may, at some point, benefit from – like a voluntary social security.

Forget about the Red Cross, which might one day pick you up from the road after a collision with a truck. Think about Oxfam, the Royal Society for the Prevention of Cruelty against Animals.

The only utility you get pout of a donation is a warm glow.

Now rerun your reasoning.

Does that help?