Both instruments might be sharing an arpeggio setting slot. In this case, you can fix this by opening the non-arp instrument, go to Arpeggio, and clicking either on the checkbox right at the side of it, or on "Select next empty slot" at the bottom.

So this happened:
I already had 1 instrument for a song in the VRC6 and did another one for arps.
I then realised that the arpeggios in the instrument settings of the first VRC6 instrument also got activated.
However, I could return the settings in the first instruments, so that there would be no arps.
But everytime I edited the second instrument it also affected the first one (the changes were somehow "transmitted" i guess one could say)

Has anyone experienced something like this before?