The subtle place we parted (I think) is where you interpreted "inherent" as meaning something about people, their feelings, attitudes, etc. I (he, really) meant it in a more abstract sense.
I'm not sure if this is something that reflects your general world-view, but you are taking a very relativist position. You are equating moral with subjective attitudes. That is OK of course, but it is a minority view.
(BTW, I'm not agreeing with the author, just commenting on the position he has taken)
Probably in the general population but I would have though it a fairly typical attitude of those who ponder these issues in depth with an open mind.
I should add that a great part of my relativistic attitude is informed by what I see as a great and inherent evil occurring in the world that apparently very few others seem to be bothered about - human caused animal suffering on a mass scale. I sometimes wonder if those who do not find this inherently bad can truly be sentient beings - but logic dictates that they are. Acknowledging that others don't share your point of view does not imply inaction in moral issues.
The place where relativist-like arguments are popular is with anthropologist evolutionist thinkers. From there perspective treating ethics as simply human traits, like a taste for sugar or music. They rarely attempt the normative leap though, go from a relativist argument to a 'you should do this' position.
Most vegetarian thinkers tend to be utilitarians. Most people are instinctively utilitarian & deontologist. When these come into conflict (kill a baby to save a village, harvest organs from unwilling person to save 5 people) they feel conflicted.
I personally think that the further you go away from direct sensation (causing pain/injury etc) the more difficult it become to disentangle inherent and learned attitudes. Even with pain their are sadists and masochists who do not seem to share the normal response.
So while arguments based on our own 'inherent principles' may resonate with others (especially those in our self selected groups) we should be very careful before assuming that these are universal.