Persians were Zoroastrian not Muslim. Thanks for your genius analysis.
You are right, this battle took place more than one thousand years before Muhammad was born. However, if Greece had been part of the Persian Empire, it might have fallen to the Arabs when they conquered the Persians in the middle of the seventh century.
Zoroastrianism was established as the state religion of Persia in c.226 BC.
Thermopylae happened 480 BC.
Thanks for your genius analysis.