For example, if a Christian makes $100,000/year and he contributes in his church 10% of that or $10,000 to it, and the IRS says alright, you only have to pay taxes on the remaining $90,000

I don't think anyone has answered this, specifically, but that is not how it works in the USA. If any person (religion aside) makes $100,000 in a year, maybe $4,000 goes to health/dental/vision insurance (pre-tax) and perhaps that person chooses to put an additional $10,000 to certain retirement plans (like a 401(k), which is also deducted pre-tax).

That leaves $100,000 - $4,000 - 10,000 = $86,000 in taxable income -- income that is taxed by the federal/state/local governments. If this person lived in my city & state, assuming she was not married for tax year 2018, she would pay about $21,509 to the federal government in taxes/social security/medicare; $4,935 in state tax; and $860 in local taxes.

That leaves, in our example (assuming I did the arithmetic correctly), $58,696 in take-home pay. Let's say she wants to then donate $5,000 to a non-profit organization, such as a church, it comes from her $58,696 in take-home pay, not as a pre-tax deduction from the initial $100k. In other words, the IRS and the state/local tax authorities are still receiving their share of taxes -- though, you can "deduct" contributions to a non-profit organization from your federal taxes, which is a whole 'nother rabbit hole.

I'll caveat this by saying that I'm not a tax attorney, so take what I say with a grain of salt -- there may be an exception to the rules that I'm not aware of.