There seems to be a growing group of people that I've started calling "virtue signalling relativists." If that sounds like a contradiction in terms, it's because it is.
Of course, yes, nonreligious people struggle with the idea of universal moral values, and they latch onto the idea that all expressions of moral values are simply opinions.
Of course though, the problem with believing that moral value systems are just opinions and are all relative is that that belief is almost entirely incoherent from the beginning. A large part of my moral value system is that moral values can be universally right or wrong. In order for you to prove me wrong and you right you have to argue that my moral value is wrong. It's self-refuting.
What's more, how to you passionately support political and social change if relativism is correct? I think that much of the support for a relativist mindset is an attempt to specifically use cultural relativism as a weapon. So, when people like me dare to criticize the human rights violations in large parts of the Muslim world, they can call me an "islamophob" because I'm daring to criticize a culture of which I'm not a part.
But, if morality is relative to culture, how can you make moral judgments about our culture? What would make our objectively better if we moulded it to your liking? If cultures are relative side by side, why aren't they relative over time?