The butcher, the banker, the drummer and then
Makes no difference what group I'm in
This line is a light play on "Rub-a-dub-dub," that weird bathtub nursery rhyme about three men in a tub.
Most variations of the English nursery rhyme "Rub-a-dub-dub" include "the butcher, the baker, the candlestick maker."
Here, Sly replaces a baker with a banker, maybe to keep up with modern times, and sticks in a drummer to make the line relevant, even to his own band. The point of the line is a little obscure at first, but the whole song ends up playing out as a listing of diverse and disparate groupings that manage to come together.
P.S. This light allusion to nursery rhymes is just the beginning.
There is a blue one who can't accept the green one
For living with a fat one, trying to be a skinny one
This way of talking about diversity and togetherness was pretty revolutionary in 1969, but by 1998, it was mainstream enough to be a Toyota commercial.
It's worth noting that "diversity" advertising has been around for a while, and Nestlé and Toyota are far from the only companies to use lots of happy, diverse faces gathered together as an advertisement for their products.
At the time Sly was writing, Martin Luther King, Jr. had just been murdered for his conviction that there was a way for people of all races to live together in the future. In a historical sense, the message of "Everyday People" was a message of political resistance, even if its cheerful hippie groove is light enough to sell candy now.
And different strokes for different folks
This line became a catch phrase that shows up in all kinds of strange places, thanks to the double entendre powers of the word "strokes."
For example, the line inspired a 1970s and 1980s television show, Diff'rent Strokes, about a rich white Manhattan family who adopt the son of their deceased African-American maid. That may be an unfortunate take on "diversity," but that's another discussion.
It's also provided a title for countless other disparate projects including golfing associations and at least one charity set up by survivors of (literal) strokes.
"Strokes," as it turns out, can mean a lot of things.
In the Family Stone context, it seems to be a slang term for something very general like "preferences." But the noun "stroke" can clearly also be interpreted as a dangerous medical event, or as a physical act, like the stroke of the golf club.
In all likelihood, Sly, who was born Sylvester and didn't get the nickname Sly for nothing, was playfully allowing "strokes" to mean whatever we think it does.