It certainly does matter to me,it wasn't until I read Fred Asbells first book and tryed solely instinctive shooting that it did become an issue for me.
I don't think it matters as much if your gaping,shooting split vision or using sights because you see where the arrow is pointing or where the sight is placed,but if the instinctive claims are as true as people that always shoot that way say,then it makes sence to me that you would shoot with your dominant eye because that would be your strongest "instinctive" eye.
After all,it is all about hand/eye co'ordination,,,right.
I personaly had no problems with getting my left hand to adapt,,,but my eye sight is not going to change,,,and once again,,,FITA target shooters use sights that give them more flexability to ignore their dominant eye,,bare bow shooters do not because we do use hand/eye co'ordination.
If somebody can give me a good reason that "doesn't" include none related methods of aiming a bow like FITA coaches training sighted target archers,then I'm quite happy to take that on board,but I'm not seeing that in any of the discussions on this topic to date either here or anywhere else.
I know there have been and still are plenty of people that shoot cross eyed dominate,as I did myself for over 25 years,and there will always be exceptions to any rule which is of course a good thing,but all the pro FITA coaches where I live all still teach dominate eye due to having no say in the issue.
Archery NZ has a very ridged set of coaching rules and the dominate eye is one thing they will not budge on,in fact any coach that steps out of that line simply doesn't coach at a national level any more,end of story on that.
As far as I can see this issue has never been "Proven" one way or the other even by those Pro coaches because I personaly know they also have differing opinions on the subject.
My father inlaw was NZ's #1 FITA coach and Naralie Fairhalls personal coach when she won Commonwealth gold for NZ during the late 70's.
He also has his doubts about this whole issue but he taught mainly dominate eye because "at the time" he had the choice and he belived it was the best over all method.
As far as I know all the better field archery and the very few that coach barebow here also teach dominate eye.
We've been fortunate to have Terry Ragsdale do some seminars here in the last few years,he came mainly to coach our field archery coaches,but they were open to any interested folks,he also taught dominant eye.
Anyway,I think we could be discussing this one for quite some time to come because it's just too personal a subject to have one answer.