Not in principle, no.
Well, when I said you should use the carbon tax for double dividend purposes, rather than to subsidize environmental projects, that could be interpreted as saying that you should use the double dividend revenue to reduce other taxes. That's consistent, but it's not necessary that you actually implement it in a revenue-neutral fashion, except for political reasons, perhaps.
My point was simply that if you have a carbon tax, it should go into general revenues, and you should go from there. If that entails reducing other taxes, so be it.