Judaism has some very specific rules regarding idols, and Jews have been around Christians for a very long time; thus this question has come up before.
Theologically speaking, we say that treating a human being as a deity is considered "idol worship", and it's generally assumed that medieval rabbis differed whether a non-Jew who worships both a non-corporeal, omniscient God along with a human being is considered doing "idol worship."
As for the physical cross itself, thank you DoubleAA for pointing to Shulchan Aruch YD141:6, in which Rama rules that a cross to which people bow should be handled like an idol (and therefore, for instance, you couldn't buy it and then use it for anything), whereas one worn is merely a symbol.
My sense is that a plain cross up in a Protestant church is probably not treated as an idol. Jews are prohibited from deriving any benefit from an idol, to the point that a building constructed for the sake of housing/sheltering an idol would be prohibited for Jews to ever use for any other purpose -- therefore (let's assume for the sake of this conversation that Hinduism is "idol worship") if a building was built as a Hindu temple and several years later they put the building up for sale, a Jew would be prohibited from buying/using it for any purpose. However, a responsum from almost a hundred years ago allowed Jews to buy an old Welsh-Scottish Methodist church and convert it into a synagogue (or house or school or shop or whatever, by the same logic) because there were no physical idols there. My understanding (and please correct me if I'm wrong) is that the Methodists have very little imagery in their churches, but they still have a plain cross.
Ask me if the same would hold regarding, say, an Eastern Orthodox church that has lots of icons ... not so simple.
The Holocaust generated (besides the overarching theological questions) a number of dilemmas relating to Jewish ethics and laws; at one point a rabbi was asked (I recall this rabbi has an mp3 about it) if a Jew is allowed to save himself from the Nazis by implying (or outright stating) that he is a Christian, the discussion involved the question of wearing a cross (just the "t" shape) vs. a crucifix (which has a picture of someone on it!); the rabbi was lenient in both cases, implying that a worn crucifix is a symbol of belief (Rabbi Rakeffet compares it to the insignia worn by a chaplain), not an idol.
Again, I can't tell you how every worshipper treats every cross in every church, but we have a few cases here that give us some starting points.
Note that all of this discussion is limited to "am I prohibited from receiving any benefit from such-and-such an item" or "what may I make use of in a life-or-death situation?" In today's liberal society it is prohibited (not to mention foolish and counterproductive) to actively damage someone else's property or body because of their beliefs, no matter how theologically wrong we feel they are.