Question: Why do Christians quote Leviticus condemning homosexuality, while they ignore the rest of the prohibitions?

Response: Leviticus contains two types of prohibitions for a precise reason. Much of the book (as well as Numbers, Deuteronomy) is given over to specific prohibitions the nation of Israel [2] was to observe as "a special people unto Me." Consistently, whether these prohibitions concern eating of particular foods, wearing of specific garments, or other ceremonial considerations, the Lord says to Israel [2], "these are unclean [or an abomination] to you" (Lv 11:7,11, etc.). This is one kind of prohibition, clearly applicable to Israel [2] alone.

On the other hand, moral issues, such as adultery, sorcery, child sacrifice, bestiality, incest, homosexuality, etc., are said to be abominations (period). Penalties against those who commit these behaviors are assessed because it is "My [God's] judgment" (Lv 18:4).