This is caused by mipmapping and not having wide enough padding between UV islands with a atlas texture.
The fix is to:
A) Disable mip maps on the texture, which will result in heavily aliasing in the texture, and possibly performance degradation. It’ll also possibly still break if you enable MSAA.
B) Increase the padding between UV islands, but you’ll still get lines once the mip level drops low enough. So you’d need to limit the mip level either on the texture itself, which requires creating the texture asset in c# as they didn’t choose to expose the option to the texture importer, or the shader.
C) Lots of complicated shader still like doing all mip mapping and bilinear filtering in the shader.