I'd argue they're incomparable. We have a Second Amendment right to defend ourselves with deadly force, but the use of deadly force on someone else is obviously not a right because it is, well, deadly.
The First Amendment though deals with speech and expression. Remember the saying you learned as a kid? "Sticks and stones may break my bones, but words will never hurt me!" It doesn't mean there are no hurtful words, but in fact is a rather clever way of noting a basic fact that people fail to take into account with the first: Speech can be ignored and we can dissociate with people. Somebody says something, they're not forcing you to do anything with it. The onus is on YOU, the listener, to make a decision to do something with that information. It is perfectly within your rights to then exercise another implication of the First Amendment, which is the right to association. You can ignore that person and block them from your life, especially in this digital age. Then they can say what they want and you don't have to listen to it. Responsibility for actions is kept on the shoulders of those who make decisions.
All that said, there is a legitimate exception to the 1st Amendment's protections known as the "true threat" clause, the definition of which I ripped from Google: "True threats constitute a category of speech — like obscenity, child pornography, fighting words, and the advocacy of imminent lawless action — that is not protected by the First Amendment."
So, the two questions here then become, "Is it illegal to not get a vaccine?" and, "Is it illegal to commit treason?"
The first is definitely, "No, though you will make your own life far more difficult by doing so." The second is a resounding yes.
In conclusion then, I vehemently disagree with you on the first and wholeheartedly agree with you on the second so long as, in either case, we're approaching the speech in question and the effects fairly and rationally.