What opinions should not be tolerated under the First Amendment?

All opinions, no matter how offensive they may be,

are and should be protected.

If you don't like what someone says, just don't listen.

No you didn't. The definition you saw was: "a person who is intolerant toward those holding different opinions." Intolerant not merely of the opinion but the person holding them. It's still not a very good definition, so I suggest you look elsewhere. As to "opinions" not covered by the First Amendment, well false statements of fact that qualify as libel or slander. Also the "opinion" that someone should go kill <insert name here> at <insert place here> is not considered to be opinion but rather "procuring murder".

The whole premise of the 1st amendment is to protect all speech.

That sounds like a liberal to me