IIRC this has been discussed several times in the forum. This is impossible to fix due to the Civ5 engine. The only way yo avoid this problem is change the mod into something which can put into the Civ5 directory directly, instead of make a real mod which need to enable from the mod menu.
Estebanium, the creator of the texture enhancement mod in this section just did that for his mod (put it into the directory instead of the mod menu), so Dylan, he'd be a great person to ask if you aren't sure how to do it.