We would be getting into the weeds of it, but it's just redistributive, with all the moral hazard associated with that, and without applying it to direct investment in a carbon sink technology that mitigates the problem.
There are values that just don't scale well without trade offs against things like human dignity (loaded, but important), and applying the sentiments behind equity to vastly heterogeneous global interests is one of them.
While I (and my more reactionary and working class friends) understand that carbon taxes presumably compensate The People for the consequences of what was formerly an environmental externality - the use of climate as just a pretext for redistribution signals what gets perceived as an underlying dishonesty and illegitimate elitism that makes it difficult to legitimize the rationale, or outcomes.
For example, basic income funded by indirect taxation is an interesting solution to a specific set of problems around technology and globalization, but it requires a level of trust that has been damaged by freighting climate with these other agendas. Still doable, but to honestly discuss the options requires frank talk about limits and boundaries to its application.
I've got opinions like anyone and I'm not always entirely above point scoring either, so it's going to take real work for people to do it.
Having read things like Jonathan Haidt's The Righteous Mind, and watching Scott Alexander's influence, the question of what the fundamental irreconcilable difference of interest may be is the most pressing question. How do we reconcile interests and coexist with people whose most basic beliefs we experience as alien? Some would just say, "win," even independent of political persuasion, but I'd argue there is immensely valuable work to be done to find ways to do better.
So short version, returning carbon tax money to the general populace means general revenue, for general spending, which is not something conservatives tend to trust.