Since synthetic fertiliser are mostly produced from fossil fuels it should be effected by a generalized carbon tax.

But I am not sold that one have to apply a carbon tax to everything at the same time. Eutrophication has turned a major portion of the baltic ocean into the dead sea and if left to continue we won't have anything left alive there for a very long time. On that environmental crisis alone synthetic fertiliser pollution need to be addressed. That it also is derived from fossil fuels and a major contributor to global warming is all more reasons to focus carbon taxes on synthetic fertiliser specifically.