It seems the Bible says that all gay people do is have sex, so why do Christians use the Bible as a weapon over one vague line in it?
Because it seems as though depending on denominations, people like to pick and choose which ones apply to real life. Why? Because the Bible has so many contradictions, it's impossible to follow every single verse to the tee. Not to mention the ones about homosexuality have been debated about for decades.
Every Bible passage I've seen about homosexuality so far is about man lying with man, not Man has a relationship with man.
Because people love single lines that sound catchy. It's not restricted to that line, that book or that faith. Hell there are plenty of atheists happy to spout a single line of Dawkins or Hitchens in order to justify hating religious people even though it takes that quote massively out of context...people just like feeling superior with a nice quote to back it up.
^Holly's right. The lines that could be interpreted as being against LGBT are called wham lines. There are less than ten wham lines in the entire book, and all of them are actually pretty ambiguous.