There is tax-exemption for donors, and for the church itself.

Without 501(c) classification, donors will generally pay income taxes on the amounts they donate. Donations would not be "tax exempt".

Non-501(c) churches may not have to pay income taxes on donations they receive, but it's much more work to determine and defend this position than just having the IRS grant a blanket exemption under 501(c).

And that's just federal tax. IRC-conformity in various states, plus cross-references to IRC in property tax and other tax exemptions, makes tax matters more or less complicated depending on where the church is located.