First, in continental Europe a big deal of clubs are not privately owned and as such can't be bought (if I'm not mistaken in Germany private owner can have only 49% of the club, the other 51% procent are "owned" by club members, this membership is open for public and attained by annual membership fee). In Spain Barcelona, Athletic, Osasuna and Real Madrid are not (and CAN'T BE) privately owned either.
Second, in an English system, which allows full private ownership, I don't get what's the problem with foreign private owners. Money doesn't have nationality, and I don't see why this would upset anyone. What I personally find "unfair" is PRIVATE OWNERSHIP of clubs, which should in my humble opinion remain/be "owned" by fans (as it is in large deal of continental clubs). But when Englishmen accept the idea that "their" club is not "their" but can be bought by some bozo with a sole purpose of personally making money with this transaction, it's stupid to oppose that a foreigner shouldn't buy it also.
What I find more unnatural then Arab/American owners, are the clubs which field mostly foreigners. If I would be a fan of an English club, I would rather prefer the club to promote as many local boys as possible, to keep the connection with the environment club exists in (not necessarily the nation, but the city or at least the region), than worry about a foreign owner. And don't say it can't be done in England, in the last game against the Atletico Barcelona had 7 starters who came from our youth academy. But what you get is this: Arsenal has more players born in Abidjan than in London. And: which club gives the most players for the Spanish NT, judging from the last selection? It's not Barcelona, Villarreal or Valencia, who manage three each, it's not Real (because its players are crap, btw), it's Liverpool with 5 players.