If people pay less in taxes, then they have more disposable income. More disposable income could lead to more charitable giving, regardless of whether someone gets a tax benefit.
I give to a few charities. I take the tax deduction as allowed by law. But I would give anyway even if I didn’t itemize and get a tax deduction.
Do big numbers of people who give to charity do so only because of the tax deduction?
I don't know. If you don't itemize deductions (about 60% of filers), it wouldn't make any difference.
I don't limit giving only to organizations with tax-deductible status.