The social media giant finds itself under countervailing pressures after the uprisings in the Middle East. While it has become one of the primary tools for activists to mobilize protests and share information, Facebook does not want to be seen as picking sides for fear that some countries — like Syria, where it just gained a foothold — would impose restrictions on its use or more closely monitor users, according to some company executives who spoke on the condition of anonymity because they were discussing internal business.