Well the connection to Butch Cassidy looks pretty straight forward. It appears he was the Grandson of Robert Parker.
But the Charles Darwin connection looks like it comes from Charles' sister Marianne who married a Henry Parker, b. ca. 1788. If he can be nailed down as a brother of Robert Parker's Father Thomas, then we have a connection by marriage. Otherwise, I'm not seeing it. Am I deciphering this right? Or did I miss another plausible link?