I can't find that Burton wrote an autobiography, though there seem to be several well-regarded biographies - have you a link to such a thing?
It beggars belief a man who was into data collecting about prostitution and homosexuality, and who helped publish extensive pornographic works to a cogniscenti married a prude, and came to jesus at the last. But the thing is, he DID marry a prude. And he DID publish works which at the time were beyond the pale, and he DID explore the darker corners of british army life in the middle east and India. The only conjecture here is the deathbed confession of faith.
He wrote memoirs, for sure. "Personal Narrative of a Pilgrimage to Al-Medinah and Meccah" I mean, thats not objective writing by title-intent, is it.
As do large dowries.