Among other things, the Freedom of Movement spell prevents an affected creature from being restrained by spell effects:
For the duration, the target's movement is unaffected by difficult terrain, and spells and other magical effects can neither reduce the target's speed nor cause the target to be paralyzed or restrained.
The Flesh to Stone spell initially restrains a creature, and then, if the creature fails enough saving throws, petrifies it:
You attempt to turn one creature that you can see within range into stone. If the target's body is made of flesh, the creature must make a Constitution saving throw. On a failed save, it is restrained as its flesh begins to harden. On a successful save, the creature isn't affected.
A creature restrained by this spell must make another Constitution saving throw at the end of each of its turns. If it successfully saves against this spell three times, the spell ends. If it fails its saves three times, it is turned to stone and subjected to the petrified condition for the duration. The successes and failures don't need to be consecutive; keep track of both until the target collects three of a kind.
Clearly, the restraining effect of Flesh to Stone would be prevented by Freedom of Movement. However, can the creature still be petrified if they fail enough saving throws, or does preventing the restraining effect end the Flesh to Stone spell, or prevent it from having any effect?
Best Answer
It would prevent petrification
The flesh to stone spell states:
In this scenario, a creature benefitting from freedom of movement is not restrained and thus does not count as "a creature restrained by this spell". As a result, they do not have to make further Constitution saving throws.
For what it's worth, a tweet from lead game designer Jeremy Crawford agrees, though his tweets are now just unofficial rules interpretations: