here are some of my thoughts, possible way of thinking:
Short answer:
Because moral (in some meaning) is not real, there is no absolutely wrong way to live, just relatively: in relation to something that you can call real (society, God or idea of God, or some teaching, or human: your leader or beloved wife). But in relation, especially if it is strong (like love), you get wrongness and rightness, maybe even in absolute forms. It sounds paradoxical, but it is true.
Interesting idea (a bit utopian, too ideal, perhaps) is deeply personal, clear moral codex. Like you can go from your PC to any website, but you need own operating system and software on PC.
Moral is (a bit roughly) an image in our minds (or souls) and sources of information. It is virtual thing, but it does not mean we should reject it, as we do not reject virtual reality and gadgets totally.
Long answer:
Your assumption is known (in philosophy) as moral relativism. Surely, it is criticised by traditional or religious worldview. I have strong interest in Catholicism. My position for your question is (maybe) not well articulated, but, roughly speaking, I am against your philosophical position. So I want to make good argument. Here what I came up with.
We want to be masters of our destiny. Relativism gives us situational ethics, so we have more freedom, more power, more opportunities. More fun. Good. We are flexible.
Pitfalls: when you are VIP (or just in subjectively important situation), you're not prepared to make fast and smart decisions. Because you have no theoretical ideal, only the situation and unarticulated properly desires. Bad.
Opposite to moral relativism is moral absolutism. Typical for closed societies. Bad.
Solution should be found in between.
Even if you have wrong (let's hope, only for some degree) ideal (codex of values), you can correct it later. (I'm inspired by J Peterson).
But what about collective moral? We may assume that modern society does not share one common moral. If it causes problems, we should seek for first principles, core ideas, values.
We cannot push our moral codex into others but we can help to open their own codexes and things that are common. Make great social contract again.
Ten Commandments are good starting point imho, as tested basis, to reflect. Using dialogue, we will find reflection of our tradition in another one and vice versa, as it was in history. But we get properly these basic principles.
Things like that can protect and develop beautiful diversity and multiculturalism. Here is smart quote: "in necessary things unity; in uncertain things liberty; in all things charity".
https://en.m.wikipedia.org/wiki/In_necessariis_unitas,_in_dubiis_libertas,_in_omnibus_caritas
So, moral relativism (which was, i tend to believe, your assumption) is wrong. It is like Scilla, Haribda is authoritarism, finding path and travelling between is the key.