I am not a lawyer, however...
I think it unfortunate that "preachy" was removed from your question. First, your use of that word, and your question's phrasing, indicates how the behavior of others has affected you. Secondly, based on the report of their actions, in a non-judgmental way, that is literally what they are, in fact doing, preaching their way of life in an attempt to convert you.
I am going to formulate my answer under the presumption that you have already tried reasonable requests, and maybe even debates with them, and the results are the same. If you have not, then use those methods first - they can lead to a better work environment for you and them. If, however, such efforts do prove, or have proven, fruitless, then stronger measures exist.
Their reported actions, and your response, suggest that their actions are actually creating what is termed a "hostile work environment." The U.S. Dept. of Labor has specific guidelines for employers to follow to remain in compliance with Title VII Civil Rights Act of 1964. One of those deals with Religious Expression in the DOL Workplace. The pertinent part reads:
B. Religious Expression Among Employees
Employees are permitted to engage in religious conversation and expression with co-workers to the same extent that they may engage in comparable private expression about subjects not related to religious issues.
Example: In informal settings, such as cafeterias and hallways, employees are generally entitled to discuss their religious views with one another. Additionally, employees are entitled to display religious messages on items of clothing to the same extent that they are permitted to display other comparable messages.
However, when such expression is directed towards other employees, such as views regarding religious practice expressed in a conversation, an employee must refrain from such expression when a fellow employee asks that it stop or otherwise demonstrates that it is unwelcome. Continuing that conduct in such circumstances could manifest into unlawful religious harassment.
Do bear in mind that while demonstrative, these guidelines are specifically for Dept. of Labor workplaces, not all workplaces. This is given as a "short form" of what the EEOC COMPLIANCE MANUAL covers in great detail in SECTION 12: RELIGIOUS DISCRIMINATION
, 12 - III Harassment
, A. Prohibited Conduct
, 2. Hostile Work Environment
, which is way too long to quote, or even paraphrase, here.
A point raised by another user, AndyT, is that veganism is not commonly considered a "religion" in the same light as mainstream religions. Depending on how it is followed and applied, it can still be considered as such under the above statutes, both as a protected practice for the adherants, and as a proscribed behavior under harassment guidelines. The EEOC COMPLIANCE MANUAL, SECTION 12: RELIGIOUS DISCRIMINATION
, 12 - I Coverage
, A. Prohibited Conduct
, 1. Religion
has:
Religious beliefs include theistic beliefs as well as non-theistic “moral or ethical beliefs as to what is right and wrong which are sincerely held with the strength of traditional religious views.” Although courts generally resolve doubts about particular beliefs in favor of finding that they are religious...
The bottom line is that what you are experiencing is "Hostile Work Environment Discrimination" and it is your employer's duty to remove that discrimination by stopping the behavior of the harassing parties.
Therefore, your next step, if needed, is to officially complain to your direct supervisor (unless one of the vegans is your supervisor, in which case you need to go up another level) about their behavior.
To protect yourself from retaliation, from both the vegans and the company, when you do choose to complain, you may wish to seek legal advice, or representation, before hand. I don't claim to know where to find the "best" such help, but you can begin with the Find Law® page on Religion in the Workplace.