There are two different things I wouldn't like, for different reasons. The first is an owner who makes the clubs a rich person's toy, rather than a business (though FFP makes that harder, where there's a suitcase full of untraceable bills, there's a way). The second is an owner who IMO has made his or her money in a more unsavory way than most: so, petrokingdoms, petrooligarchs, etc.
I can't imagine supporting another club. But I think I would grow steadily less enthusiastic if we had an owner who fit either or both of the above bills. Parts of what I find so compelling about Spurs are that they're always a long shot to succeed, and that, all things considered, they're a proper club, run the right way, with players who seem like a remarkably decent bunch for a collection of rich young athletes.