Like I said, it is complicated and up for debate. I have heard many conflicting viewpoints about it. Some take the whole bible literal, including the literal laws of the old testament - and they are not just a few, but many, many explicit laws about everything. More are mainly literal about the 10 commandments. And for some the only law is Jesus saying: "Love other people like yourself".
Since being raised catholic, I know quite a lot about the bible and less about the coran, but as far as I understand "With Christian rules, it's easier to find excuse to augment or re-interpret them." this is possible there as well, as Mohammed also said conflicting things, was softer in the beginning and harsher in the end, so you can also pick what you like. Hijab for example is not an explicite rule. And about Homosexuals, well, you probably won't find anything tolerant in the coran about it, but I think you won't find something in the bible either. What matters to me, is what people are doing.