“Paul was wrong about a lot of things so we don’t have to go by what he said.”

No

Peter, the one chosen by Jesus to be the lead apostle had this to say about Paul’s writings:

Bear in mind that our Lord’s patience means salvation, just as our dear brother Paul also wrote you with the wisdom that God gave him. He writes the same way in all his letters, speaking in them of these matters. His letters contain some things that are hard to understand, which ignorant and unstable people distort, as they do the other Scriptures, to their own destruction. 2 Peter 3;16,17

Peter calls Paul “our dear brother”, said that Paul wrote “with the wisdom that God gave him”.  He refers to Paul’s writings as “Scriptures,” saying that those who distort them are “ignorant and unstable people” who are headed for destruction by doing so.

Some protest that Peter’s “opinion” isn’t a good example because he was “always saying the wrong thing.”  The Bible is unique in not hiding people’s miss-steps, even sins.  However, none of the inappropriate things that Peter said (Matthew 16;22,23; 17:4) were for our instruction but only his reactions to the utterly new things he heard and saw. Even if Peter had instructed the wrong thing, that would give us no reason to doubt Paul.

Of course, Jesus is the better witness:

But the Lord said to Ananias, “Go! This man is my chosen instrument to proclaim my name to the Gentiles and their kings and to the people of Israel. Acts 9:15

Jesus sought Saul of Tarsus/Paul out and appeared to him personally to call him to be his follower.  Jesus chose Paul to proclaim his name to us so we pick and choose what we observe of Paul’s teachings* at peril of rejecting Jesus’ commands.

*Perhaps a few things are only for their culture but probably not as many as people think—and everyone seems to have differing opinions on this.