Of course we should profile, at airports, for instance. Not all Muslims are terrorists, but all terrorists are Muslims so why the hell are we strip-searching grandma?
As to the illegal immigrant problem, there's an easy and relatively inexpensive fix. Issue biometric ID cards to all U.S. citizens - include your driver's license info on it as well. Without one, you cannot fly, interact with a bank, obtain employment, secure medical, educational or any other gov't services, buy a house, rent, etc. etc. At the same time, make it a felony for anyone to offer such services or otherwise engage anyone who does not possess such a card. Unable to work or function in this country, illegal immigrants will migrate back to where they came from - we don't even have to round them up and put them on buses, etc.
This also will create huge employment opportunities for out-of-work Americans. Employers will be forced to pay a living wage to Americans, instead of off-the-clock, below-min. wage to illegals, or (as they should) go out of business. This bullshit about illegals doing jobs American's won't is true only because Americans won't pick cabbage for $2 an hour. But they sure as hell will for $10 an hour.