So, you say that these words are important because they are descriptive. I disagree. The words are only descriptive because you have not given us any specific, concrete actual examples. You need to show, not tell.
Show, don't tell is a technique often employed in various kinds of texts to enable the reader to experience the story through action, words, thoughts, senses, and feelings rather than through the author's exposition, summarization, and description. The goal is not to drown the reader in heavy-handed adjectives, but rather to allow readers to interpret significant details in the text. The technique applies equally to nonfiction and all forms of fiction, literature including Haiku and Imagism poetry in particular, speech, movie making, and playwriting.
Show us how they are acting rather than ascribing adjectives to them that each person can interpret as they wish. This gives us a better chance to really understand your situation. Someone who is a vegan may assume your terms are hyperbolic and opt to argue with you about your interpretation. This doesn't help you get an answer, it distracts from your question, and leads to confrontation.
So, tell us a story (a true one). Paint us a picture that maybe even convinces other vegans that your coworkers are a bit over the top. Make it clear to us that their behavior is unwelcome. You don't need to call them names to do this! Your question will be infinitely more detailed if you show us what is going on rather than telling us.
As an example, instead of "pushy" you might say something like "they have been talking to me at lunch every day for the last week even after I asked them to leave me alone and it's making lunch uncomfortable". You've done a better job of explaining the situation in this meta question than in your actual question.
You don't need the words "pushy" or "militant" to explain your situation. Let your situation speak for itself and let readers decide from the concrete examples what an appropriate response is. You will get better and more useful answers and (hopefully) fewer people merely interested in a framing challenge.
As a side note, Stack Exchange has one rule - "Be nice". Recently there was even a Meta Stack Exchange discussion about whether non-users must also be treated nicely - they do.
To quote from the chat transcript I linked to earlier:
honestly I'm pretty much just flat offended every time I hear the word "preachy" for exactly the reasons I detailed here. Truthfully what would be better than an answer is if the question is closed until the OP writes a specific situation they are confronting and removes the baited language in it ("preachy", "off my back", arguably "militant" insofar as I'd rather hear about their actual behavior). In the meantime I really don't like reading other answers exploring the preachiness of these vegans when the interpersonal error is buying into that stereotype in the first place.
If your framing is making people uncomfortable because you are using terminology that is problematic and "baiting", it's time to change the way the question is phrased. Note that djechlin is specifically asking for the question to give concrete examples rather than using this phrasing. And I would say that their request is reasonable.
One thing we forget and that is important to Interpersonal Skills in particular is the thought, "just because it's true doesn't mean it's okay to say".