If an incorporated church does NOT have a formal 501(c)3, are donations to them tax deductible?

It is not a recognized charity. It may even be the pastor's sole proprietorship; there's no way for us to know. A church that is part of a recognized denomination will fall under it's blanket but independents have to file on their own.

All churches are considered eligible charities for the purpose of tax deductibility of donations and tithes UNLESS the IRS has specifically withdrawn the church's tax exempt status. Even if the donations are ultimately used for purposes outside of the church's ministry (and is therefore taxable income for the church) the donations are still deductible by the parishioners or members of the church.

Should you make a donation to a church whose tax exempt status had been withdrawn by the IRS, you simply cannot deduct those donations or tithes. From that perspective, yes, you would pay income taxes on those donations simply because you could not use them to reduce your taxable income.

A church does not need 501(c)3 status in order for charitable donations to be tax-deductible.

I see you have researched the issue, and you have the correct information. But, the fact that churches are automatically recognized as 501(c)3 organizations in the way they operate does answer the specific question regarding charitable donations, specifially, that they are tax deductible.

Some income to a church is taxable, some is not. If you have made a charitable donation to the church, and it is used for church purposes, it is not gross income to the church.

if you read those publications, 1023, 1024 and 1026, churches are not required to get the 501(C)(3) status but they do need to have an EIN which they annotate on their correspondence to you if you contribute $250 or more during the year