I'm not exactly sure how a standard hotel room contract works, but assuming I am renting the room and have ownership-like responsibilities for everything in it, is it a problem if there is a Gideon's bible in the room? What about other non-Jewish religious items, like a picture/statue of Buddah?
In regards to whether you have ownwership with a rental.
The entirety of the hotel belongs to the owner of the hotel, including the rooms that we, the guests are renting from the owner, so when I carry around the hotel I am carrying within the property of that owner. The room I rent in the hotel is not my property unless it is a long term rental and all the movable object belong to me, otherwise I am simply a guest in his home. Rabbi Chaim Tabasky
This was in response to whether one can carry on Shabbat from ones room to another's room without an Eiruv Chatzeros.
- Gideon's Bible
One should not daven facing a mirror or painting. According to some authorities, if there is a Gideon Bible in the room, it should be placed in a drawer prior to davening Derech Pikudecha (Lo Sa'aseh #11: Hagah), Shaylos U'teshuvos B'tzel Hachochma 2:84.
- Whether such paraphernalia is considered avodah zara at all.
Paintings/Pictures of Avodah Zara (here a cross is referenced). Source here
If there is a picture or painting that contains within it a cross or similar item, even though it wouldn’t be considered bowing to a cross, it is still best to be stringent and not [daven, learn or] bow in the direction of such a picture.(Psak of Rav Chaim Kanievsky Shlita)
In regards to the objects of Buddhism, they are definitely considered avodah zara.
It is my understanding that Bhuddists actually worship the statue of Bhudda, in which case the statue is forbbiden and should be destroyed. I have seen major poskim quoted to this effect as well.Certainly it is forbidden for a Jew to own such a statue. Chaim Tabasky
However, there is a discussion of whether idolatrous images as art are considered avodah zara. Look Here
Rambam, Avodah Zarah 6:7, which rules that if the status is made for show, and not for idolatry, it is permitted to derive benefit from it.
Tur (Yoreh De’ah 141) writes that if in doubt, the idol/statue is forbidden
Taz (141:2) writes that this is only true under circumstances of itchazek, meaning that there is concrete reason to suspect idolatry.
Although Shach disputes this, today the vast majority of statues are made as works of art and not as idolatry, and unless one has concrete reason for suspecting otherwise, there would be no prohibition on keeping the statue.
However the above only applies to being lenient in profiting from a sale and ownership(cf. Look Here above). So whether its a problem to own them at all is debatable.
These are all generalities though, any action taken should be consulted with a qualified Orthodox Rabbi.
It's all hotel property (or it may even belong to some religious group, not the hotel), not yours. So it's not your problem. The best thing to do is just ignore it.
Here's a quick test: if you were out at a conference and lightning struck the hotel room and burned it down, would the hotel expect you to pay for a new bible? Of course not! (If you damaged their property, that's a different story.) Not your responsibility, property-wise? Then not your responsibility, religion-wise.
The Talmud talks about owning Chametz on Passover; there were Jews who had to store food for the Persian army in their houses. The arrangement was that the Jews had financial responsibility over it, i.e. if the house burned down due to lightning strike, the Jew would be expected to replace the food. This means the food is the Jew's responsibility, and thus if it's Chametz, he couldn't have it in his house on Passover.