I recently talked to a US theologian, who just got a job in a really difficult market. He was reflecting on the challenges facing theologians. You can either work in a secular university, in a religious studies department. Those jobs generally discourage you from making any normative claims, or recognizing religious authorities. Or you can work in a religious college (a so-called confessional college, which is founded upon a confession or creed - in practice almost always some Christian denomination). This sort of job does encourage you to make normative religious claims, but polices those claims to preserve their particular religious identity. There are a few university divinity schools that successfully avoid confronting theologians with this dilemma, but such jobs are far and few between. So jobs at confessional colleges are a theologian's most realistic shot at stable employment.
A theologian needs to be careful about the views she's exploring. My interlocutor's new employer was interdenominational, which typically means they'll have a more liberal stance toward doctrinal issues since they can't follow one particular line. But still, he said, you've got to be cautious - test the waters, consult with other faculty members, to see how far you can go.
This suggests that the case of infringements on academic freedom where people are fired because they say Adam and Eve aren't historical people, or the case of Thomas Oord* more recently (see here and here) aren't just outliers, but part of a greater problem of lack of academic freedom for the majority of US theologians. How can theologians do cutting-edge work if they have to fear for repercussions all the time?