"It's raining outside, you need to take an umbrella with you when you go out."
I think "...你出去要带雨伞" should be accepted too but I would like to hear a native speaker's opinion. Would it sound weird to say 雨伞 instead of just 伞?
Yes, it is a bit weird in actual use. But it is definitely a valid sentence.
It does not sound weird, but it depends on area which one is more common. Both should be considered as correct.