Although the answer of Natick, Massachusetts is correct, this could probably use a little more explanation, and since I live two towns over from Natick, I'll give it a shot. Natick was founded in 1651 as a Puritan-governed settlement for Native Americans who generally had been converted to Christianity (known at the time as,"Praying Indians"). The settlement declined after King Philip's War (around 1675), when the Native American residents were interred on an island in Boston Harbor (with many deaths), and the village was largely destroyed during the war, but the settlement still existed throughout the Revolutionary War. In 1719, a plot of land was purchased for use as a burial site for the local Native American residents, and about 20-25 of the people buried there were veterans of the Revolutionary War. However, after the war, the settlement began to disappear -- but the burial ground was considered sacred, because (since the "Praying Indians" were indeed Christian) it was consecrated ground, so it survived the collapse of the native village.
And then, after the U.S. Centennial in 1876, most towns in Massachusetts (which had just erected large monuments to their Civil War veterans) started to erect memorials to their Revolutionary War veterans. Well, in Natick, the Native American burial grounds was overwhelmingly the largest burial site. But there was a dispute about how to build a monument that wouldn't disrespect the native burial grounds, Eventually, though, the town monument was erected on those grounds in 1900 (as mentioned in the question), prioritizing the Native American Revolutionary War veterans who had been buried there.
https://natickprayingindians.org/warriors.html
https://www.natickhistoricalsociety.org/first-praying-indian-village