The main body of the Yeoman Warders (the correct name for Beefeaters) eat nothing but beef morning, noon, and night.
However, the ancillary regiment, The Queen's 5th Yeoman Instant Mash Lancers are all vegetarian, and also gluten-free.
They are not to be confused with the Quorn Hunt, which is a bunch of posh country-types that ride out with hounds and cruelly hunt down and rip to shreds innocent little veggie sausages.
Even though the name Beefeater came from giving Yeomen a daily ration of meat - I expect there must have been or are some vegetarian Yeomen/Warder - soon to be Yeowoman/Warder!