OP. I don't think it was clearly stated whats going on with your question.
Every once in a while, Nintendo updates the firmware for the GC Slot itself. The GC Slot has it's own firmware and efuses. If the system firmware sees the wrong fuse count you get the error. In essence, your Game Cart slot is tied to a certain firmware range.
To avoid the error, and protect efuses, CFWs disable the slot.
In Atmo, to disable the Cart Slot you turn NOGC to ON. SX has the GC slot disabled by default.
If you want to use the slot in Atmo you disable NOGC, enabling the GC slot and bringing efuses up to date for that System firmware. If NOGC is enabled, it does not matter whats in the slot because it's inactive.
SX has no option to turn the GC slot protection off and on. Instead SX keeps the GC disabled unless a cart is inserted.
When you start with the cart in SX with the 11.0 EmuNAND, and the GC slot is updated past that, the firmware sees the efuse discrepancy and errors out.
Nothing you can do.
Install the cart and eliminate the need for the GC slot to be active in SX or remove the cart before switching to SX.
That's your options.
BTW, i truly recommend getting away from the file based EmuNAND. They are known to corrupt. This can cause you to lose all of your data and in general cause a huge headache. Instead use Dual Hidden Partitions. They are far more stable, faster and the are a much better long term solution that isn't susceptible to Ninty's crappy drivers and allocation issues.
I have a guide here
https://gbatemp.net/threads/how-to-...en-partitions-on-the-same-sd-tutorial.601607/
It's easy, takes time to process things but the hands on time is next to nothing and you'll be better off. You can shrink the SX EmuNAND too if you like. I use Super XCI for all my SXOS stuff. That way the game updates and DLC are in the XCI and can be easily and neatly stored on a USB device ready to be mounted.
I moved all installed games to Atmosphere, SX is for USB loading only on my setup. The EmuNAND is just for save games and firmware at that point. It will reduce the actual time the switch access the EmuNAND and reduce the amount of space that SXOS eats on your SD. I have gone with 8GB and never run out of space on my SX EmuNAND.