Ideally you want the triangle to occupy a set of 2x2 pixels at its smallest like the image on the left in the grid was one grid size larger. If the triangle only occupies a sliver of pixels whose area is not a 2x2 square it causes overdraw like the image on the right. All red pixels are considered when drawn which causes…
I'd weld it, soften the edge and offset the mirrored UVs by one unit so that they don't contribute to the projection but still occupy the same space in the texture.