I would imagine that the Clintons mailed invitations to everyone who wrote them a check without really looking into who these people are. "Look, a $1000 check from some preacher in Kansas. Make sure he gets an invite!"
Does anyone really think that Bill and Hill and Al and Tipper are in cahoots with Phelps? When those photos were taken on the LCR site, Al probably barely knew who the man was and figured some no-name preacher's support would look good to blue-collar, conservative democrats.
Phelps' notoriety came later. You can be sure he won't be invited to Hillary's inauguration.
You are woefully misinformed. Phelps has been "preaching" hate for the last 50+ years.
He was a voting delegate to the DNC in 1996, and invited to the Clinton/Gore 1997 Presidential inauguration.