Even if we just shoehorn them into abortion services. There are many services people who do not believe in and are receiving tax dollars this is no different. Aka churches, oil companies, war the list can go on forever.
Churches don't get taxes. The get to reduce the money they owe the IRS for donations, mostly because the government recognizes that churches do a large number of things that benefit society and the communities they serve.
Homeless shelters
Soup Kitchens
Public service projects
Hospital visits and volunteering
Food, clothing and other drives to help victims of natural disasters
Lots of their service overlap the things government tries to do. I understand if you didn't know any of this. You'd have to go to church to find out about all the things the accomplish in the name of "pushing their opinions on others."

War? The government has few specific duties mandated in that Constitution you like to wave around. One is the duty to provide for the common defense, raise Armies and establish a standing Navy. War is the government's monopoly. Bill Gates or Exxon can't declare war on a foreign power.
Technically, we are not at war in Iraq and Afghanistan. That was a sanctioned UN effort to combat terrorism. We (the US) did not issue a declaration of war to any of these nations' leaders. So "War" is not a valid description.