"Congress shall make no law [...] abridging the freedom of speech [...]"

This is not related to 1st amendment; this is no law being passed by congress or any government body. Nothing prevents a person from speaking after an NDA is signed - they won't get tossed in jail, because no law was broken. However, after doing so, they will be responsible for any civil penalties they agreed to when they signed the contract.

I only brought in the first amendment to highlight the importance of the right to free speech. Contracts are important but perhaps some things should not be allowed in them. Many contracts are unfair, but people enter into them anyway for various reasons.