Cart only loads fuel of the kind it is using at the moment, even if it doesn't have any in the inventory.

Best explained with an example:
I was using wood as fuel, I replaced the fuel in the fuel station and removed the wood from the carts fuel inventory.
It didn't pick up the new fuel, I believe because the fuel bar still had value although there was no fuel in the inventory, mined the cart and put the new fuel in it worked correctly.

You're right on the cause, but the best approach to take isn't clear to me here.

I'm hesitant to make fuel behaviour too complex lest it end up like AutoFill which cheerfully puts wooden power poles into burners, because they have a fuel value.

I understand the concerns, would it be possible to filter the fuel slot just like you filter the equipment slot? that way you might even be able to switch fuel by sending signals through the constant combinator.

Example: You filter fuel to coke, if it has wood in the fuel slot when the cart reaches a junk unload stop it would unload the wood and on the next fuel stop load only coke from the chest even if the chest also as wood in it.

Fuel is a LuaInventory https://lua-api.factorio.com/latest/LuaInventory.html but I don't know if it can be filtered in the UI. I've never tried.

Switching fuels with an additional command signal would be possible to implement, though, even without a visible filter.

So for example, if you add a sticker for "fueling station" with a slot, the fuel placed in that slot would be loaded in the cart if available, If no selection is made it loads anything with a fuel value?

It would work ok I think.