Being a vegan or a vegetarian is completely okay in Islam, but the problem comes if one thinks that eating animal products is immoral or haram. Allah says in the Quran, “O believers! Do not forbid the good things which Allah has made lawful for you, and do not transgress. Indeed, Allah does not like transgressors.” (Quran 5:87). Therefore, if one wants to follow this lifestyle, that is fine, but one shouldn’t think that this way of life is better than what Allah said.
And Allah knows best.