In the past during droughts, I’ve heard they require stoves that have an on/off switch, so no alcohol or gel fuels. Esbit may also be excluded.  White gas would be a reasonable step, because I think the risk is higher, but I haven’t heard of it. It’s very rare, such as during Santa Ana wind conditions in SoCal, that they stop you from using propane or iso-butane canisters.
the latest US Fire Service restrictions for Los Padres don’t have any of this:Â Â https://www.fs.usda.gov/detail/lpnf/home/?cid=stelprdb5401877
PCT hikers may appreciate the low snow pack now, but for us year-round Californians there will probably be a lot of restrictions until our (potentially) rainy season late next fall.