Is it legal and is it appropriate to display religious items in faculty offices in the United States? This question is specifically in the context of an American public institution and a generic faculty member, specifically not someone working in religious studies or a similar department. I have noticed over the years that many faculty members have religious items on display in their office or on their office doors, and I was wondering on the one hand whether they are legally allowed, and on the other hand how wise it is to display them while being sensitive to a diverse student population. Here are a few examples from my own experience (all in mathematics).


Several years ago I had a colleague post the ten commandments outside his office  door. 
I have another colleague who has Bible study books prominently
displayed on his bookshelf.
I myself have a poster of the Buddha and a Buddha statue in my
office, both given to me by a student.
Somewhat less on topic: a now-retired faculty member used to put ads
for a Bible study that he held in his home in graduate student mailboxes. (I know many foreign graduate students found this off-putting.)
There's a big difference between inconspicuously displaying religiously-themed materials in one's office and effectively proselytizing, as the retired faculty in your example apparently did. The former is I think entirely reasonable, as it's a personal display that does not put any burden on a visitor or guest to the office. Putting religious materials in their inboxes is unwanted, and is inappropriate for a faculty member to do (particularly given the power imbalance involved).

I don't think I've ever received (or heard of) a legal notice that one is not allowed to display religious imagery in a personal office. Is it a good idea? Again, I think it's a question of degree. There's nothing wrong with displaying a small cross or Star of David or moon and crescent in one's office. Having a large and ostentatious display, though, would probably put students ill at ease. Similarly, having those materials where you actually meet with students (say, at a conference table in the office) is more "aggressive" than just having it on a bookshelf.