Does having private views that marriage should be between a man and a woman justify the government firing you?

How is having a private view that marriage should be between a man and a woman be any of the government's business? Whether one thinks that it is a good idea to believe that isn't the issue. Obviously if someone advocated homosexual marriage, this wouldn't cause any problems. I am pretty sure that unlike private employees, government employees were supposed to be covered by the first amendment. From Fox News:

A former “Teacher of the Year” in Mount Dora, Fla. has been suspended and could lose his job after he voiced his objection to gay marriage on his personal Facebook page.
Jerry Buell, a veteran American history teacher at Mount Dora High School, was removed from his teaching duties this week as school officials in Lake County investigate allegations that what he posted was biased towards homosexuals.
“We took the allegations seriously,” said Chris Patton, a communication officer with Lake County Schools. “All teachers are bound by a code of special ethics (and) this is a code ethics violation investigation.”
Patton said the school system received a complaint on Tuesday about something Buell had written last July when New York legalized same sex unions. On Wednesday, he was temporarily suspended from the classroom and reassigned.
Patton said Buell has taught in the school system for 22 years and has a spotless record. Last year, he was selected as the high school’s “Teacher of the Year.”
But now his job is on the line because of what some have called anti-gay and homophobic comments.
Buell told Fox News Radio that he was stunned by the accusations. “It was my own personal comment on my own personal time on my own personal computer in my own personal house, exercising what I believed as a social studies teacher to be my First Amendment rights,” he said. . . . .