All tax paying citizens should have a say in the workings of their government and would be unfair and discriminate to disallow immigrants who have gone threw the naturalization process the right to vote. It would also be removing a large part of the population opinion and possibly skew the views of the government on its citizens if a majority of them had no say.
Aliens, even if legal residence, are not required to speak English or understand how our political system works. Permanent resident cards are granted to refugees and spouses of Americans. There is no way to make sure that they are making an informed choice unless they have taken classes in English and US Civics, either in public schools or as part of a citizenship class.