That’s how I read it, because otherwise the second sentence wouldn’t make any sense. He’s saying that
Changing ‘which’ to ‘that’ wouldn’t change the ambiguity of the first sentence at all. Adding commas around ‘which stifles black self-determination’ would lead to this:
“The black theologian must reject any conception of God, which stifles black self-determination, by picturing God as a God of all peoples.”
Would also be ambiguous; could look like the writer was saying that the black theologian should reject any conception of God, which would be an unusual pice of advice for a theologian.
Rephrase it both ways by moving just one clause:
Your interpretation:
“The black theologian must, by picturing God as a God of all peoples, reject any conception of God which stifles black self-determination. Either God is identified with the oppressed to the point that their experience becomes God’s experience, or God is a God of racism….”
Your friend’s:
“The black theologian must reject any conception of God which, by picturing God as a God of all peoples, stifles black self-determination. Either God is identified with the oppressed to the point that their experience becomes God’s experience, or God is a God of racism….”
Which tallies better with the second sentence? To me it seems clear that it’s your friend’s interpretation. Picturing God as a God of all peoples would not mean that ‘their [the oppressed’s] experience becomes God’s experience.’
Or at least, it kinda would, in the sense that God would have the oppressed’s experiences as well as everyone else’s, but it’d be meaningless; why bother saying that God’s experience is of the oppressed as well as the oppressors? I mean, that’s old hat - it’s not something worth writing down as a point of contention.
In your longer quote, the writer refers to God being black, to Jesus being The Oppressed One, Israelite slaves being the people of God. It definitely looks to me like he’s saying that God is for and from the oppressed only, not the oppressors too.
Maybe you could email the writer and ask? His wording really isn’t clear, and he might be interested in clarifying, you never know.