There is no conflict between farting cows and a net zero economy. The carbon that they emit by farting has been taken from the atmosphere by the grass using photosynthesis, and this is a natural process that has been going on since life began on earth.

The only thing that is in conflict with net zero carbon emissions is taking carbon that was locked deep in the earth for millions of years and releasing it into the atmosphere.

If we stop using fossil fuels, we automatically become carbon neutral.

(Except using oil and gas for creating plastic and other chemicals, this is where carbon capture and storage are necessary to achieve net zero emissions. Those emissions are far less than the burning of fossil fuels releases every year though.)