Printing money specially for community purpose and specially for real business is taxless situation not "tax on owning money".
Why would no one want that money if it is a separate part that finances common interest and real business (money created at the time of need)?
Printing money for just community purpose will be no different from the current system where people are just looking at how to avoid or pay less taxes in different ways, which again that earnings from taxes does not end up 100% for the purposes it should go.
The inflation would be the same and value of money would remain the same with the same monetary policy, only the way of financing common interest will changes and the real business sector gets true freedom.
Inflation could be controlled mathematically with issuing and with coin burning.
I think that taxless society can be possible with just more transparency and with more math.
Inflation wouldn't be the same, it would be much much higher, because you'd have to print much more money then now. And this whole system would be unfair, because everyone would be hit equally - both the poor and the rich will lose money. Currently someone who is unemployed and doesn't have an income is not paying many taxes, but in your world they'd have to deal with huge inflation, which is really hard for poor people, as they live from one payment to another.