It seems clear to me that the logical outcome of the first precept is a vegetarian diet...the problem comes when the person adopting that diet becomes a Vegetarian with a capital V. They then build a whole new non existent personality around being a Vegetarian with a capital V. Including quite often an apparent need to proselytise to everyone else.
So that while observing the logical outcome of the precept, they undermine themselves by becoming judgemental and prescriptive about what others put in their own sandwiches.
Which seems to miss several points.
Pointing out the logic of a vegetarian diet from a number of positions is one thing.
Using vegetarianism to create an "us and them " is quite another. I think the more mature Buddhist cultures of Asia recognise that . But some western Buddhists struggle with it.
The going for refuge is the door of entrance to the teachings of the Buddha.