I do not know of any data on the exact prevalence of moral relativism, but we can examining societal behaviors.
Societal behaviors that correlate with moral relativism would be
1)The Rise of Big Government (you only need government when people disagree over values)
2)Decline in marriage. Egotism results in the decline in marriage.
3)Multiculturalism. Multiculturalism is impossible to justify from an objective moralist standpoint.
4)Growing restrictions and/or the looming threat of restrictions on freedom of speech in Western countries. Only people interested in pursuing power believe in limiting freedom of speech.
5)The decline in the significance of the philosopher.
6)Decline in the meaning of music. Music without meaning (objective purpose) can never amount to high art.
7)Populism and pandering in politics and business.
Rather than having a society revolving around objective morality which serves a long-term purpose, todays laws and social norms are about accommodating and fulfilling people's personal wants.
An example is premarital sex. In 2016 we have a society that glorifies engaging in this. This is caused by the nature of human society at large. So this happening could be seen as inevitable, but it may be seen as a disregarding of virtuous and family values in favour of accommodating people's immediate yearnings.