Non-profits benefit by their status, allowing them to not pay taxes. They have resources paid for by other citizens, including fire and police protection. Other citizens pay for these resources by coercion, though they may not necessarily subscribe to the aims of the non-profit, whether it be a church or a planned-parenthood center.
Next time I'm asked to give to a non-profit, I should say that "I give at the office." It would be a true statement (if I had a real job).
Sometimes non-profits decide to persuade others to think as they do. This might be to accept Jesus as their lord and savior, or it might be to use every means available to keep a pipeline from being built. Again, this points out the problem of forcing individuals (through taxes) to support an organization that might be advocating for a position that is not their politics of choice.
Some might think the non-profits might sink if they did not get this support. Some will. Others will enjoy a new freedom, where they can now support political action and candidates to their hearts content. And they might get more support from like-minded individuals.
The new revenue to the government hopefully will be returned to the citizenship, rather than to enable the government to become still larger. With the citizenship having more money falling out of their pants, hopefully they will give more charitable contributions than they did before.
And should these individuals be able to deduct their contributions? No! That is just another example of the government supporting the non-profits by subsidizing individuals who give to it.
We could transition to this new status to free non-profits over a number of years to give them time to develop a new base of support.