I practice using both dominant and non-dominant hand grips when shooting around cover/barricade on either side.
Some help from a qualified instructor can often help identify and address exposure issues when shooting from behind/around cover materials.
You might be amazed at the unnecessary exposure offered by some folks who think they're making effective use of a cover situation (standing, kneeling, etc).
Also, it can be surprising to see the number of folks who don't safely clear the cover material with their muzzles, or who allow cover/weapon contact which interferes with proper functioning (usually without being aware of the actual cause of the stoppage/malfunction).
If a rifle/shotgun is involved, sometimes the type of sling used may limit of hinder being able to switch from dominant to non-dominant. Again, some range time with an instructor versed in the commonly encountered various equipment options, as well as familiarity with the anticipated role planned for the weapon's use, might be helpful when it comes to choosing and using a sling.
While there are always going to be exceptions and mitigating circumstances which come along (usually unexpectedly, it seems) I tend to try and retain control of a weapon with my dominant hand/side. Why not work to my greatest strengths and to maximum advantage in adverse, difficult situations?
Injury, or having to simultaneously perform another critical task which requires my dominant hand, are why I include non-dominant hand shooting in my practice and drills, and still recommend it occasionally be included in periodic quals in my role as a firearms instructor. Naturally, safety requires that someone be properly versed in the skill before being tested or allowed to practice it on their own, as with any other firearms-related skill.
Retired LE - firearms instructor & armorer