I might argue that we do follow the OT, we follow the entire bible. We do not follow Jewish law and that is the difference. The NT fulfills the OT and looking at it from that perspective, we are obedient to all of God’s commands. He, after all, is the author of the entire Bible. Jesus was raised a practicing Jew and perfectly executed the faith. If we are to live in the image of Christ then there is not a contradiction in obedience to all.
That being said, you may run into specific areas like consuming what is not clean. I believe Jesus said not to call unclean what the Lord has made clean.
There is also the issue with not keeping holy the Sabbath. Well the Church, in her Authority given by Christ, has moved the Sabbath to the Lord’s Day.
I’m sure there are others but, I am also sure that any proposed contradictions between the OT and the NT are from interpreting scripture independently from the authority of the Church.
God Bless,
Michael