I never got why it would upset religious people. It doesn't even mock Jesus. The one thing it offers a truly scathing satire of is the radical left of the 70s.
It's mostly that at the time the film came out there was usually an orchestrated backlash against anything even vaguely controversial organised within about five minutes of it being broadcast/shown/advertised/mooted as a possibility. Mary Whitehouse and all that. I mean, a few years later there was even an outraged debate in the Commons about The Singing Detective (which can be read here).
Ooooh, so chockfull of quotable bits!