My memory was that it came out at the end of a football interview when the interviewer asked him about his religious beliefs (nothing about Eileen Drury).
As for being "utterly ludicrous", there a millions of people around the world who are part of religions that share his view of reincarnation. You might find it ludicrous but it doesn't mean it isn't a genuine religious belief.
Clearly his religion (or rather the hysterical reaction to it) lost him the England managers job. You mention it requires an image of cleanliness - the point is that whether someone is clean or not seems to depend largely on what the current (I mean this weeks) opinion of the 'great british public' is - usually spurred on by a press agenda.
Hoddle's great crime was not holding the conviction of his beliefs but by being nieve enough to answer a question honestly.
I feel that's wrong - it should just be about whether he can do the job or not (ps. I think the same for JT).