Clarification: I'm referring to the system of segregation that was affirmed under Plessy v. Ferguson and fought by MLK: separate bathrooms, whites-only restaurants, separate and almost universally worse schools. Were there any African-Americans who thought that a "separate but equal" system would be an acceptable state of affairs?
This is late but there was a big debate in the 1970's within the black community about whether integrated or (voluntarily) separate institutions were an ideal way to foment black uplift. It's covered in Tanner Colby's three part series for Slate on integration. Part 1 is here but this issue is addressed in Part 3. It starts being covered around this paragraph:
By the time King was assassinated in Memphis, the civil rights movement had reached a critical crossroads: Integrate or separate? Fight to get in or resolve to stay out? On this question, there is a fantastic issue of Ebony magazine that ought to be required reading for every American. It was published in August 1970, and the headline on its cover reads: “Which Way, Black America? Separation? Integration? Liberation?” The whole issue, front to back, is filled with essays and reportage on black America’s splintering coalition. Read as a whole, it’s a fascinating back and forth between mainline integrationists from the Urban League and the NAACP, on the one hand, calling for the complete dismantling of Jim Crow and the shuttering of black institutions to facilitate a migration into the larger society, and militant black nationalists on the other, demanding total separation from white American oppression, an embrace of Afrocentric art and philosophy, community control over black institutions, and the financial reparations necessary to make that possible. Back and forth, they argue, page after page, resolving nothing but giving a crystal clear picture of the problem at hand.
By the 70's, either late in the civil rights movement or "after it", after the slow failures of the movement to achieve many of the desired changes, this tension existed not just between radicals and moderates but within individuals. It became a major tension as "Black Power" grew in power. It's not like the Black Panthers wanted segregation or Jim Crow... but they realized that integration wasn't a panacea. They therefore sought to set up not "segregated" institutions but "their own" institutions. This tension has largely, but not entirely, faded from civil rights discourse.
But to make it clear: these people didn't support "separate but equal". These were people who thought the system was so top to bottomnracist that it wasn't worth participating in, that there could never be equality in system designed by "the white supremecy" so why even bother trying?