Theistic morality

[The Omnissiunt One]

People's wellbeing (and that would include non-humans) is the best basis for moral judgement, IMO.

That's a relative moral judgement. I might share it, but it still is relative. That should pose no problem at all, as long as we acknowledge that fact and don't hide it under the carpet with fancy names like 'consequentialism'. In fact facing it head on should provoke new thoughts from a sceptical critical thinker in the same way as you do in this one sentence where you say "and that would include non-humans". For that in fact is a critique of the more common statement that "People's (as in humans) wellbeing is the best basis for moral judgement". In this one sentence you show how relativistic moral judgement enables moral progress.

I like that "IMO" addition to your sentence. It shows the relativism...

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PS: Beside the goal that you use to base moral judgement IMO there are others that need to be added because they don't necessarily follow from your goal. For instance, that autonomous, critical thinking is a valuable asset for everyone.

I wasn't just trying to use fancy names. These are generally accepted philosophical terms. From Wiki:

Moral relativism may be any of several descriptive, meta-ethical, or normative positions regarding the differences in moral or ethical judgments between different people and cultures:

Descriptive relativism is merely the positive or descriptive position that there exist, in fact, fundamental disagreements about the right course of action even when the same facts obtain and the same consequences seem likely to arise.[1]
Meta-ethical relativism, on the other hand, is the meta-ethical position that the truth or falsity of moral judgments, or their justification, is not objective or universal but instead relative to the traditions, convictions, or practices of a group of people.[2]
Normative relativism, further still, is the prescriptive or normative position that as there is no universal moral standard by which to judge others, we ought to tolerate the behavior of others even when it runs counter to our personal or cultural moral standards.[1

As for consequentialism:

Consequentialism refers to those moral theories which hold that the consequences of a particular action form the basis for any valid moral judgment about that action (or create a structure for judgment, see rule consequentialism). Thus, from a consequentialist standpoint, a morally right action is one that produces a good outcome, or consequence. This view is often expressed as the aphorism "The ends justify the means".

I've no problem with admitting that my morality is relative in the sense you mean it -that it is relative to each situation- just not that it is relative in either of the latter two cases cited (meta-ethical and normative). Also, autonomous critical thinking is generally better for everyone, as science has been the crucial force in improving our lives. There is a case to be made for blissful ignorance, I suppose, and I'm not sure I regard rationality as good in itself... but most people would rather not live in false hope if possible (though perhaps organised religion suggests otherwise).