Shirts that are made with a flat bottom hem are meant to be worn untucked. But if the shirt has visible “tails” — that is to say, the hem varies in length, rather than being even all the way around — it should always be tucked in. Wearing a shirt with tails untucked is not a forbidden look. But it is a juvenile one.
With nothing else on the upper body, it makes you look like a teen rebel at a grown-up wedding. Under a jacket or with a suit, being untucked makes you look like you’re trying too hard to be stylishly rumpled.