In Judaism, some religions are considered to be Avodah Zarah, and others are not. So, for example, if Christianity or certain of its denominations is Avodah Zarah, that has implications for Jews' interactions with those religions and with their places of worship.
Islam also distinguishes between religions which are Ahl-ul Kitab and ones which are not.
Does any major Christian tradition make similar distinctions, or does Christianity generally merely treat all non-Christian religions as non-Christian?