No more than usual. Civilisations change their moral habits all the time. Once we though it immoral to refrain from hanging murderers, now most of us believe the opposite. In my lifetime I have heard gossipping women excusing a man imprisoned for molesting a little girl on the grounds that "At least it's normal," - by contrast with those disgusting homosexuals who did unspeakable things to other grown men! Now of course the reverse is the usual moral response.
The test (in secular, social terms) of a morality is whether or not it works; whether or not it creates conditions in which the mass of people may live fulfilled lives. It is clear that a huge variety of systems might do this, if accepted by the people of the community.
Even religion, despite its claim to be eternally valid, usually progressively bends its rules as time goes on. We no longer burn heretics, for instance, and the churches' attitudes to family and sexual life are not what they were even 50 years ago.
What we should rightly be terrified of is any moral system, religious or secular, which fails to adapt to changing circumstances. Having no choice, we must live in the world as it is, and regulate our behaviour appropriately - we cannot, and should not try to preserve outdated systems of ethics.