Q. Does charitable deduction offset your ordinary income first before long term capital gains?
A. Simple answer: Yes.
As with all tax questions, the real answer is: It depends!
That said, for most people, the EFFECTIVE answer is, yes charitable deductions offset your ordinary income (the income taxed at the highest rate) first, before offsetting long term capital gains (LTCG). As others have said, LTCG are part of your AGI and the LTCG portion of your taxable income is not broken out on form 1040. But, LTCG are broken out (unreduced by deductions) on the "Qualified dividends and capital gains worksheet" (or the Schedule D worksheet) and taxed at LTCG rates (which may be 0%).
