Say you let someone in who suicide bombs himself and takes out several Americans. Then a reporter asks the DHS spokesperson how they let someone in the country that had "Death to America" posts all over their social media out in the open for everyone to see but they didn't. Nobody would forgive the government for such a grave oversight.
At the airport you already let them check your luggage and pockets to make sure you're not a threat to the crew and passengers. How's it different to be checking your social media before entering to make sure you're not a threat to the citizens?
Which do you think is more important to the electorate, the safety of the citizens, or the privacy inconveniences of immigrants, which doesn't exist anyway?