I believe this condition was reported in version 1.2.9 and fixed in 1.3.17 (latest build). Have you tried the latest build?
Yes I have the latest version..
Doing a quick test I see that, with Enterprise Browser v1.3 active in background, datawedge profiles are disabled (you cannot scan in DWDemo or any edit field like the browser search box).
In Details, there's a non-editable DataWedge profiles that disable datawedge when Enterprise Browser is active. You should contact Zebra support to open a case if you need a different behaviour.