ArXiv submission and LaTeX compilation
Upload the libraries that you use, along with your LaTeX source. This will ensure that your system and arXiv are compiling your source using the same libraries (rather than different versions of the libraries), which should ensure similar results (any remaining differences are due to the compilation process).

This solution bloats the upload to arXiv. Bloat can be partly avoided by only uploading troublesome libraries. Alternatively, you could try specifying versions of packages.