This seems to be a non-power-of-two texture issue. Specifically WebGL1.0 does not support NPOT textures with mipmaps. Does your source texture have Generate Mip Maps enabled by any chance? If yes, try to uncheck it.
Yes, I believe NPOT textures with mipmaps should be supported in WebGL2.0 (Firefox and Chrome already have working implementations of it, though you might wanna wait for support in other browsers as well).