Imported from GitHub PR https://github.com/abseil/abseil-cpp/pull/1589

It makes sense because even if it fails spuriously, we can just try again since we have to check for other readers anyway.
Merge 0b1780299b9e43205202d6b25f6e57759722d063 into 6a19ff47

Merging this change closes #1589

COPYBARA_INTEGRATE_REVIEW=https://github.com/abseil/abseil-cpp/pull/1589 from AtariDreams:atomics 0b1780299b9e43205202d6b25f6e57759722d063
PiperOrigin-RevId: 595149382
Change-Id: I24f678f6bf95c6a37b2ed541a2b6668a58a67702