Do white accessories as a guest count against the rule?

I think that would be fine since the dress isn't all white. You could ask the bride how she feels though. As a bride i'd be fine with that, it's adorable

The dress seems fine. The hat looks a bit bridal and I've never seen anywhere wear a hat to a wedding unless it's derby-themed or cowboy hats for men. But I think both are fine.

Not wearing hats to a wedding is definitely an American thing. Her wedding is country-themed, and cowboy hats are encouraged, so I figured it works with the Southern/picnic vibe. Maybe If I pin some colorful flowers to the brim, it'll look less bridal?

Right, I'm an American, so that makes sense I haven't seen it. I think if if cowboy hats are encouraged, your hat is fine. I'm sure people will wear straw hats that are also basically white.