The GSS has data on religious self-identification extending back through the early seventies up to the present. The following graph traces, by year, the percentages of non-Hispanic whites, non-Hispanic blacks, and Hispanics who indicated they had no religious affiliation. The mean sample sizes by year are 1112, 126, and 108, respectively:
Understanding there is some noise present in the year-to-year sampling, the white irreligious rate has been higher than the NAM irreligious rate has been over at least the last several decades. While the ratio hasn't changed much over the time period in question, the fact that the irreligious proportion of the population has gone from being fringe at the margins to the sizable minority that it is today probably makes the racial disparity more recognizable now than it was then. In the seventies, someone with no religious affiliation was so rare--and the proselytizing shrillness of New Atheism not yet a thing among them--that most people's pattern recognition software didn't pick up on the racial characteristics of non-believers. Today nearly one-in-five whites professes no affiliation, so if a person knows a handful of white guys, there's a good chance he knows at least one atheist or agnostic. And among an average person's facebook social circle there are tens or hundreds of people without any religious affiliation.
GSS variables used: RELIG(4), YEAR, ETHNIC(1)(2-3,6-15,18-19,21,23-27,32-33,36)(17,22,38)