In ArcMap 10.6 how can I turn off the 'snapping' associated with drawing rather than features?

Do you have any features that do not have a symbology (e.g. they are symbolized based on a category, but you don't have some of the classes symboloized and have the All other values option turned off).

I've found that in some of my larger MXDs, this can cause issues with snapping and I'll end up snapping to these un-symbolized features.

If that's the case, the easiest way to fix it would probably be to use a definition query to remove the other layers. If you only have a few classes, you can do something like "Field In ('class1', 'class2')".

In the option (the general ArcMap option, not the feature snapping option, see first picture) there are 4 different setting for snapping one of these are "grid" (the other are guide, ruler and margin) you could try to disable all of them, if that still doesn't work you could try to set the snapping tolerance to a very low value.

In the feature snapping option (second picture) there are setting to activate basemap snapping and feature service snapping and again a snapping tolerance setting

By checking all of this you should be able to solve your problem

(picture are from 10.3 version so there may be some difference with your, and as it's in french my translation for the option may be off...)