We should simply ignore the externality all together because we're all paying for it anyway.
Either the subsidies take into account the carbon tax or they don't. If they do then it's number rearranging. Government gives dollars and then immediately takes some of them back, it's a convoluted appropriations bill. If they don't then food prices go up which is contrary to the government's goal of keeping food cheap at the point of sale.
If you want to reward reducing carbon emissions by giving additional dollars or paying for more expensive but better for the environment equipment then that could potentially be effective.
Trying to reduce a negative by pumping resources into a positive rarely works out as expected and often has surprisingly distortionary effects. (see ethanol and corn production in the USA)
I’m personally of the opinion we should be doing far more tying together of revenue neutral taxes and subsidies within an industry. When you want to reduce a negative externality you tax that and then redistribute the proceeds equitably back across relevant actors. When you want to increase a positive externality, you equally tax actors and then distribute it asymmetrically according to the behavior you want to encourage. Or combine the two approaches to address both negative and positive externalities in one go.
These approaches allow you to be more targeted, while minimizing overall market distortions.
It’s not exactly number rearranging, even if the government increases subsidy payments to offset the cost. E.g. say gasoline costs twice as much per gallon due to a carbon tax, but subsidies are increased proportionally to offset the cost increase so that food prices remain constant. This still creates an incentive for farmers to use “cleaner” forms of energy as the ones that do will increase their profit margins. Ultimately the increased subsidy is a burden on the tax payer, but in a more narrow sense carbon producing farms would be subsidizing some of the costs for farms that produce less carbon.
Whether this plays out as intended remains to be seen. I think externalities need to be priced in somehow, the issue is determining the appropriate cost. If you want the market to decide the cost efficiently there needs to be some mechanism to tie the two measures together (increased environmental quality => lower carbon tax rate). I agree however that manipulating the economics of food production is dangerous and needs to be done slowly and carefully.