Is it illegal to speak out against Obama at press conferences?

No, it is not illegal. However, it is rude and unprofessional. No matter who the president is, a reporter is not there to "speak out against" the president. Press conferences are for the media to ask questions and get the president's reply, so that the reporters can file the story for their newspaper or TV station or wherever they work. The press conference is not supposed to turn into an argument. That said, sometimes reporters don't feel they got enough of an answer and they might shout out another question, but most professional reporters understand the reason for a press conference and they conduct themselves in a manner appropriate to their job.