All (or at least almost all) native English speakers learn both manuscript and cursive writing and by adulthood have developed their own style of writing that is one or the other or a combination of both (I and most of my family and friends write in this way - mostly manuscript but certain letters are always in cursive and joined together - whatever is fastest and smoothest).
Cursive is used almost exclusively for signatures, even if a letter or note was written in manuscript.
Some English Language Learners ONLY learn to write in cursive. I am a teacher and have taught in Nepal and Thailand, and my Indian students have never learned manuscript.
Although cursive is not as prominent as it once was, I still think it is an important thing to learn if you are hoping to really master the language and "fit in" with native-English writers.
If you are looking for an easier cursive script to learn, I'd recommend trying D'Nealian. It is based on manuscript letters and so has simplified many of the curly-cues that cursive writing is known for. It's the one we teach our students at school, and I've had kids go from not being able to read or write cursive AT ALL to being perfectly adept at it in just one month. Give it a try! It can't hurt to learn it!