And: Would they be ok with their government having no funds but other governments being still funded by taxes.

Publicly funded armies replaced hired mercenary forces for a reason.

This is heavily dependent, probably even correlated, with the way the government currently uses taxes. For developed nations this is a no-brainer, of course they need the taxes to supply services to the population.

For developing nations? I know a few countries were the government having little to no funding would make very little material difference to daily life, since they already steal so much public funding that private services have long since filled the gap. In this case the percentage for caring about tax payment is zero, or close to it

Governments (with monetary sovereignty) are not funded by taxes they are currency issuers, this is a fallacy.

Yes, I hope they wouldn't exist and that people would setup new companies to replace governmental service (for a voluntary fee).

Read about agorism (konkin) and anarchocapitalism (rothbard, friedman).