No, that depends on the content of the movie and if it is licensed.
MP4 is a movie format that can be used legally for legal content, there are a lot of downloads of movies that are free of copyright on the Internet Archive for example.
Also Youtube uses MP4 internally as one of a couple of formats, Apple Movies uses MP4 (but with a DRM), Amazon Prime and maybe also Netflix use MP4. All this is legal.
If you are downloading pirated movies on Bittorrent, these will likely be MP4, which would be illegal but not because of the format but because the content is unlicensed, it would be illegal as a WebM or MPEG2 or AVI file as well.
Also, if the content of the movie is illegal like illegal pornography, the MP4 would be illegal, but it does not depend on the format itself.
