I would go one step further and say that donations to religious organizations should not be tax deductible. They are not charities in 99% of the cases.
You said 99% of the churches do charitable work. I highly doubt that’s 99% of budget. I am sure most of it is used for operations. Just because I make donations every year, doesn’t make me a charity organization.
(Not an American)...I don't see any need for donations (religious or non-religious) being tax-deductible. In my country, it's very simple: here's your income and here's your tax rate (no deductions). What you do with the rest is up to you.
Many countries find it useful to encourage some behaviors and discourage others by means of tax policy. Not just the US, although the US seems to do it quite a bit.
So we have, or have had, tax policies in the US that encourage home ownership, marriage, donations to charity, long-term investment, purchasing electric vehicles or electrifying your house, and more. The results of each of these is mixed, and sometimes contentious, but they're all there because congress decided at one point or another that a thing was worth encouraging or discouraging.
(an American) - our tax code encourages behavior society deems virtuous. We "want" people to give money to homeless shelters, outreach programs, overseas disaster relief, etc - so we "push" then to do that by making it relatively less expensive.
I can easily argue that citizenry being directly involved in directing their funds to causes that matter is more democratic than the government doing that on their behalf.