Not at all, they're directly at odds in this case. The President using presidential authority to restrict what twitter can say on their own platform is directly violating the first amendment to restrict twitter's free expression.
You can argue that twitter is also restricting others' free expression, but that is their right, while the government preventing twitter from doing so is a 1A violation.
You can argue that twitter is also restricting others' free expression, but that is their right, while the government preventing twitter from doing so is a 1A violation.