It is not at all accurate. The 3%er myth is a bad faith argument that takes the 80,000 pension applications for Revolutionary War service filed after 1818 and divides it by the total number of Americans in 1776, estimated to be 2.5 million people. From this, a figure of 3.2% is derived.

But of course, just for a start this 2.5 million figure includes all children, the elderly, and the disabled, who physically could not fight. And half the population were women, who also were legally not allowed to join the military. And then you add to it that a signification significant proportion of the 2.5 million Americans were enslaved people who were legally disallowed from serving, so the actual number of Americans qualified to fight was much lower than 2.5 million.

And then the 80,000 pension applications were only filed several decades after the war, since the pension system was not fully put into place until 1818. Before that, only war widows and disabled soldiers qualified for a pension. After that, then any soldier who served could apply, or their widow, but in the case of the soldier, A) only if they were still alive and could prove their service, or B) in case of the widow, she could prove her husband's service and she had never been subsequently remarried after her husband's death. Thus, 80,000 only presents a small fraction of men who served in the war. Modern estimates generally say that there were hundreds of thousands of men who served in the war.

Anyway, I give a more comprehensive answer here with a two-part follow-up here. /u/uncovered-history has also answered the question here.

In short, it's a bad faith argument that has no reasonable basis in reality, except to mislead. On the contrary, when you actually compare the estimated number of people who served the Revolution versus the subset of Americans who could have qualified for military service (i.e., able-bodied white males between the ages of 16 and 59), then the Revolutionary War likely has the highest participation rate of any military conflict in U.S. history, going back to the country's colonial roots and forward to the present day.