The problem with this question is that there is no one fixed set of "New Age" doctrines, in the sense of something like the official magisterium of the Roman Catholic Church. Absent any repository of doctrines, one can only speak of "New Age" as a term applied collectively to a series of religious and spiritual movements that arose in wealthy western countries in the second half of the 20th century. Many of these belief systems were based on neo-pagan or eastern religions, but often modified through the lens of fiction, popular culture, or the beliefs of individual charismatic leaders. Many New Age groups did have absolute moral beliefs. Some were strictly pacifist and vegan. Some were completely opposed to personal property. Others followed complex systems of communal lifestyle with marriages and sexual activities regulated by a leader or guru. So all one can really conclude is that some members of some New Age groups accepted certain absolute concepts of right and wrong, others had different absolute concepts of right and wrong, and many had no absolute concepts of right and wrong as a defining feature of their New Age philosophy (though they may or may not have had them as part of an individual moral system).
While I would not consider myself New-Age, I am from what many would call an alternate spiritual background, and I have a somewhat pantheistic worldview.
There are basic principals of moral belief, such, don't kill, don't steal, don't cause pain, don't lie, don't cheat.
What of these things is absolute wrong?
How many of us eat meat? It has protein and nutritional value that we need to survive, so killing is not an absolute wrong, we slaughter animals because we need the resources they provide to survive. Plants are also living things, and we eat those too, or use them for medicine.
Of course to kill for pleasure is what a moral person would consider an absolute wrong, but then we have the game and trophy hunters who kill for sport rather than survival? Would we say this is wrong?
Many would (and I'm talking about more than just Peta).
As far as stealing, there are circumstances that would make you reconsider the morality of it, someone stealing food to feed their family when they are desperate. We can understand why.
Many of us as a general population would say this is wrong, but it is instinctual to have a will to survive, so would we take a loaf of bread if we were starving? If someone was trying to kill us would it be wrong to fight for survival?
Circumstances can turn morality upside down. Is it wrong to kill or steal for selfish gain? Of course, but if it is strictly for survival, what is or isn't moral?