It's Constitutionally impossible to strip a natural born citizen of his citizenship. Naturalized citizens are fair game.
This opens an interesting gambit though. In order to discourage American citizens from renouncing their citizenship the Obama Administration has increased the fees to $2,500, a massive increase. If this measure passes, all people need to do is send a $1 donation to ISIS then send a copy of the donation to the State Department and wait for them to strip you of your citizenship.
Clarification
Though you can find assertions on a number of sites on the Internet to the contrary, a natural born citizen
may lose his citizenship due to acts of expatriation, as these are regarded to be willful acts of renunciation. In other words, the people via Congress may insist that a person has in fact renounced his citizenship, whether that person formally declares his intent to do so via official channels or not. The person's act of expatriation
is the formal declaration of his intent.
However, under most circumstances the State Department would not issue the certificate of termination prior to formally interviewing the person in order to determine his conscious intent.
But we are talking about an especially grievous act of expatriation in this instance. In my opinion, as one steeped in immigration and nationality law, including the pertinent constitutional, statutory and case law, the government would have sufficient grounds to issue a certificate terminating the citizenship of those shown to be fighting abroad for ISIS/ISIL, though the government's likeliest course of action would be to apprehend/kill these miscreants aboard or apprehend them here should they try to reenter the United States, charge them for treason and then, perhaps, upon conviction, issue a certificate of termination.
Scroll halfway down:
http://www.state.gov/documents/organization/109065.pdf
Also, the following site has it right:
Can a natural born us citizen have his citizenship revoked against his will
The law prohibits the taking of your citizenship against your will, but there are certain actions a citizen can take which are classed to be a free-will decision that constitutes renunciation of their citizenship. Which means if you commit these such acts you are willfully agreeing to the loss of your citizenship.
The ways to lose your natural born US citizenship are detailed in 8 USC 1481:
1.Becoming naturalized in another country.
2.Swearing an oath of allegiance to another country.
3.Serving in the armed forces of a nation at war with the U.S., or if you are an officer in that force.
4.Working for the government of another nation if doing so requires that you become naturalized or that you swear an oath of allegiance to that country.
5.Being convicted of committing treason.
Also, the case law regarding expatriation/renunciation of U.S. citizenship:
http://michaeldavidrawlings1.blogspot.com/2009/12/iwong-kim-arki-meet-irogersi.html
Under:
http://michaeldavidrawlings1.blogspot.com/2011/03/righting-confusion-of-citizenship-and.html