If you suppose that morality foundationally requires objective values and that such values can only be provided by God, then I suppose that as an agnostic you are in a quandary about the foundations of morals. But in the first place, objective values conceptually do not presuppose the existence of God. Plato argues for such values in the Republic and elsewhere and they are embodied in the Forms eide, which are beyond the realm of sense but, except on a heterodox reading, in no way logically or metaphysically dependent on the existence of God or gods. May be and most likely the Forms are fantasies but conceptually they are not self-contradictory, so logically could exist, and could do so without the prop of divinity.
It is also conceptually possible for God or gods to exist who have no concern with morality. This is the case with the Epicurean gods who dwell in the inter-mundial spaces and have no commerce with or interest in the tediously imperfect world of humanity. There are, I assume, no Epicurean gods but again their existence is conceptually possible, so God or gods logically could exist without any concern to provide the foundations of morality. They have better, self-concerned things to do.
So : conceptually there can be objective moral values without God or gods; and God or gods without any divine basis for morality.
If morality is a matter of doing what one thinks one ought to do, and refraining from the opposite, of considering other interests besides one's own, I fail to see why it cannot be a pure product of our attitudes or emotions. I save your life because I have an attitude of sympathy; I save your life because thereby I obey a divine command or because my action corresponds to some eternal value of the Platonic kind. In each case I do what I think I ought to do. Why look deeper than that ?
Of course, the objection is raised that attitudes or emotions are blind, accidental, variable between individuals, a surd element in human life. But this is a caricature. I cannot have an emotion without having certain beliefs. I cannot - logically cannot - be angry with you unless I think you have done me unjustifiable harm. So moral emotions are tied to assumptions about facts, about what you have done in the case of anger. Am I not open to argument about the facts? You provide adequate evidence that you did not do what I think you did, and logically my anger must disappear. Emotion and reason interlock.
This view, once termed obviously enough 'emotivism', has acquired the new moniker of 'expressivism', probably because it is plausible to base ethics on both emotions and attitudes; and moral judgements can 'express' both. Attitudes next, then.
Suppose I have an attitude of moral disapproval towards persons with a certain sexual orientation. If facts can be produced that make it reasonable to believe that such persons do not choose their orientation voluntarily but have it for causal reasons beyond their control, then as a rational agent I must relax my disapproval because it relied on false assumptions. I may continue to dislike the orientation in question or become indifferent to it. Either way, I cannot rationally maintain my attitude of moral disapproval. Attitude and reason interlock.
A morality of emotions and attitudes can sustain ethical agreement and, when disagreement occurs, leave morality open to rational discourse.
Such a morality fits with agnosticism as with much else.
Irrealism in Ethics (Paperback).
ISBN 10: 111883741X / ISBN 13: 9781118837412
Published by John Wiley & Sons Inc, United States, 2014.
Values and the Reflective Point of View: On Expressivism, Self-Knowledge and Agency.
ISBN 10: 0754654125 / ISBN 13: 9780754654124
Published by Routledge, 2006
Or - quickest and probably best first option - look up 'emotivism' and 'expressivism' on the online 'SEP'- 'Stanford Encyclopedia of Philosophy'.