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.
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)