There is no such prohibition. However, there are offsets.
- Contributing to an IRA may result in a reduction of the QCD amount you can deduct. (The aggregate amount of deductible IRA contributions you make to your IRA after you turn 70 1/2 will reduce the amount of the QCD that is not includible in your gross income.)
From <https://www.fidelity.com/building-savings/learn-about-iras/required-minimum-distributions/qcds>
PUB 590:
Offset of QCDs by amounts contributed after age 70½.
Beginning in tax years after December 31, 2019, the amount of QCDs that you can exclude from income is reduced by the excess of the aggregate amount of IRA contributions you deducted for the taxable year and any prior year that you were age 70½ or older over the amount of such IRA contributions that were used to reduce the excludable amount of QCDs in all earlier years. See the Qualified Charitable Deduction Adjustment Worksheet in Appendix D.
Example.
Jim became age 70½ in 2019 and deducted $5,000 for contributions he made in 2020 and 2021 but makes no contribution for 2022. Jim makes no qualified charitable distributions for 2020 and makes qualified charitable distributions of $6,000 for 2021 and $6,500 for 2022.
He determines he has no excludable qualified charitable distribution for 2021 as figured on his 2021 QCD Worksheet. His 2021 qualified charitable distribution is reduced by the aggregate amount of $10,000 of the contributions he deducted in 2020 and 2021, which reduces his excludable qualified charitable distribution to a negative amount of $4,000.
Jim decides to make a qualified charitable distribution of $6,500 for 2022. Jim completes his 2022 QCD worksheet by entering the amount of the remainder of the aggregate amount of the contributions he deducted in 2020 and 2021 ($4,000) on line 1. This amount is figured on his 2021 QCD worksheet and is entered on line 1 of his 2022 QCD worksheet. Jim figures his excludable qualified charitable distribution of $2,500 on his 2022 QCD worksheet ($6,500 – $4,000 = $2,500).
https://www.irs.gov/publications/p590b#en_US_2021_publink100095352
