In context and less shit translations, it's pretty clear that he's saying he's fulfilling the prophesies and the promise of the old covenant, not that literally he's changing nothing.
In the same context, you have him saying that the entirety of the law is to love your neighbor as you love yourself.

Or, more bluntly from the same story:

Before the coming of this faith,[a] we were held in custody under the law, locked up until the faith that was to come would be revealed. 24 So the law was our guardian until Christ came that we might be justified by faith. 25 Now that this faith has come, we are no longer under a guardian.

I have now googled more Bible shit than I care to to cite my dim recollections of religious history studies.
Tldr, Jesus supposedly came to fullfil the promise of the old testament via a vis the relationship between man and God, and to replace that covenant with a new, more chill covenant with less shellfish and more love.

And, this is important to your point, a lot of flaying people alive for failing to obey their slave masters or properly worship God. You don't have to cite the old bit of the book, that they believe is obsolete, to find gnarly shit that makes it not look great.

It doesn't feel too ridiculous to me that religions that came about in the same area would reference each others texts, but aren't beholden to be responsible for their content. 1000 years of telephone was not kind to that translation.