I believe as long as the protests are peaceful and respectful then people have the right to protest the building of the religious buildings, I believe everyone should be respectful of some ones religion but I do believe these people should have the right to protest the building if they feel like that's the right thing for them to do.
Anyone can protest peacefully, but what reason is there to specifically protest the building of a school or 'church' (I'm not sure of the correct terminology for each religion) for muslims? Wouldn't it be better to just accept people and their religion so they might accept you? Why do we lean so naturally towards discord and enmity?
Communities protesting the construction of Muslim schools and mosques may not be conscious of their bigotry, but that doesn't mean they are not bigoted. The vast majority of Muslims, especially those who live in the United States, are as peaceful and normal as the average Christian, and their rights are protected.
This becomes a clash between freedom of religion and freedom of expression. I would also say that this involves property rights. If a group purchases land, gets the right permits, and pays the right taxes, I think they should be able to put up whatever kind of religious center they want. The community has the right to protest within a reasonable distance, but peacefully. Eventually protesters run out of free time and move on, or get violent. Lets hope for the bored option.
As new ethnic groups have come to America, they have all been subject to some level of discrimination. Boston, now so much an Irish city, once had workplaces that said, "No Irish need apply." But every group that has joined this great project of freedom as served to make us stronger. It will be no different for Muslims. "Give me your tired, your poor, your huddled masses yearning to breathe free." The words on our Statue of Liberty define what America is at our best.