This looks like a Northern Waterthrush to me. The throat isn't clean white, the streaking below looks to be too heavy for Louisiana, there's some yellowish tint in the supercilium, the bill is on the smaller side and the legs are pretty dull.
Looks more like a California Gull. Westerns don't get that far inland. You're just seeing the underside of the feet, which often look pink even on yellow-legged species. The wings don't look dark enough for Western, neither do the underwings. The white trailed edge to the wing is also a lot...
This is a Bushtit. It's not chunky enough for Wrentit, the bill is too small, and they are unlikely to be foraging in the open with a group of warblers. Wrentits are also restricted to more natural shrubby areas, you generally won't see them in small parks or neighborhoods.
Rufous are fairly common migrants and winter residents in Texas now, while Allen's are still very rare. This looks like a young female, which are essentially identical, and tricky to tell apart even in the hand.