Well said.
This is as belligerent as Putin’s take-over of Ukraine. 
To avoid paying taxes and to attempt to get your elected leaders to change how that money is used are two different things. As far as paying for other things that should be considered morally questionable, I would say there is always room to examine how our tax dollars are being spent and to voice our concerns to our leaders. And finally, two wrongs don’t make a right. Under the logic from the op, if you sin in one way you’d might as well go all out. Lied about being sick to get off work? Well, you had better support your friend when he tells you he cheated on his wife. And you and your friend had better not say anything when you see someone getting mugged on your daily jog.
We elect people to determine what taxes should pay for. In our country there is not majority support for having the government pay for abortions. Of course given the propensity of Catholics to support abortion with their votes this could change
It’s unavoidable. From being a contributing member of society the output of some of your efforts or flowing into supporting the others in the same society. Resources and services typically are not segregated by the moral and political stances of the people that consume them. Even a person that does nothing more than bake bread could find that his food is consumed by those that make policies he disagrees with. And he is in some way also supported by those people when they money they make is used to purchase his bread.