A failure mode of environmentalism is attaching it to random other progressive ideas. "Let's have a carbon tax and use it to fund universal healthcare!" I want a carbon tax, and I want universal healthcare, AND I want them to be completely disjoint. I will argue for each independently on their merits.
Otherwise both magnify each others' vulnerabilities. For example, say universal health care is funded through a carbon tax, and this tax works really well and emissions plummet. Now universal health care suffers? What a stupid outcome!
Robust government programs are independent with separate funding (see Social Security). Make a big carbon tax, have it fund an equally big carbon dividend, and run it independently from everything else on the progressive or conservative wish list.
This cuts the other way too. No, a carbon tax should not fund conservative pet projects like eliminating capital gains. That has to live or die on its own merits, not tied to environmentalism. The carbon tax must be its own thing to endure.