In many issues there are charities on both sides, fighting a zero sum game, for example pro-choice and pro-life charities. If they both have less money the end result in policies being enacted probably won't be any different.
Tax exemptions create legal complexity and distort incentives (e.g. big 4 have tax minimisation service lines which is a waste of money and talent). Getting rid of all tax exemptions is a good idea, and removing the charity exemption is a step in this direction.