There are numerous ways to finish a quilt. A birthed quilt presents as a knife edge finish which is perfectly acceptable. Facing is also acceptable.
I would be more concerned with how the quilt behaves itself for you in the quilting process when birthing. Birthing tends to cause issues with the shifting while quilting, resulting in pleats or puckers either on the front or the back. But if you are confident with doing it there isn't any reason you can't.
If you have any doubts you should consult the show's rules to see if there are any rules against it. I have never seen any but there could be shows that stipulate binding finishes only.