Near Beer and PSC

I was diagnosed with PSC in 2011 and my condition has been stabilized with ursodiol. Obviously, I don't drink alcoholic beverages anymore, but I occasionally indulge in a near beer (like O'Doul's) and Fre alcohol-removed wine. The label says these drinks contain less than 0.05% alcohol content. Has anyone discussed this topic with their doctor? Any medical opinions on this issue? Just wondering.