Everyone has a self serving moral fluidity that bends to ease their own conscience. What it the purpose of morality if it exists only to be bent or broken?
How do you know "Everyone has a self serving moral fluidity that bends to ease their own conscience", as opposed to "Every one has a perfectly rigid and consistent morality but they lie when then talk to others about what it is"?
In the second case, which I suspect is the more likely the morality you're referring to (the one which people talk about) serves to signify membership of a social group to which the speaker wishes to belong, the membership requirement being that one claims to adhere to said moral principle.
The purpose of actual morality is to be able to make choices which are most likely to bring about your own happiness even in circumstances where the consequences are too complex to be calculated and so previous experience or the experience of others must be relied upon.
Equally near the opposite ends of Western philosophic history, Diogenes of Sinope and Nietzche would both clearly agree with you on that.
In The Gay Science, Nietzsche several times refers to 'actually moral people' as 'monsters and scarecrows', because he sees any moral system that could be elaborated or explained as so rigid that it must necessarily either ultimately cause massive harm, or reduce its adherents to non-thinking manikins.
It is the essence of his 'Perspectivism' that every individual has some part of the truth missing from all others' viewpoints. Therefore every person has an obligation to change morality, to re-evaluate values and change their valuations, at least a tiny bit, or they serve no moral purpose whatsoever and simply constitute 'herd beasts'.
Diogenes founded Cynicism on the basis of a Delphic assignment to 'deface [all] the currency'. He first attempted to do this literally, by destroying mint equipment. But when that did not pacify the oracle, he realized that it was a moral imperative: that 'currency' (the original Greek term translated, as well as our word in English) meant 'what is now popular' as well as 'passable coinage'.
From this point of view, equally, whatever is the current morality will always be lacking and will need to be 'defaced' by those who can see through public opinion. Given some of the things he is recorded as saying about food, sex, art, etc., part of that change is adapting rigid rules to fit personal preferences.
For either of these thinkers, necessarily, that bending morality to suit oneself is an integral part of the purpose of morality itself.