Mod wheel in EXS24

Yes, some instruments have articulation switching by the mod wheel built in.

If you do not want this functionality, you'll need to open the instruments in the EXS editor and edit them to remove articulation switching, and save them as new instruments.

Or, easier still, don't use CC1 for setting up user controls, use different CC's (you can always realtime transform your mod wheel into a different CC if the mod wheel is your only accessible controller).

Use a transformer in the environment to convert CC1 to a different CC before the MIDI data hits the instrument.

(I may or may not be using the pitch bend wheel also, would that interfere with this method?

The pitch wheel is completely independent from the mod wheel - two different things.

If so I'd like to know how to remove the articulation switching in the instrument (in this case just the standard general "Flutes" sample with EXS24

Open the instrument in the EXS editor. What you'll need to do will depend on the complexity of the instrument and how it's laid out. Go and have a look, and familiarise yourself with how instruments are defined. If you get stuck, post back. To be honest, if you're not into sampler instrument editing, I would not do this, and just convert your mod wheel to something else, or better still, use Logic's quick automation access assigned to the mod wheel to control any selected plugin automatable parameter.