If you ask people whether or not they think grammar is important, they will stare at you for about a minute before answering: "Why, of course it is." Or, they might answer: "It don't be."
I don't think I truly learned grammar until I taught it to myself as an adult. No, don't respond by wagging fingers and badmouthing the educational system. Instead, ask yourself if knowing grammar (being able to recite rules and diagram sentences by drawing roadmaps that would make sense only to the most medicated) really makes a difference.
Language is intuitive.
We learn by sound. We hear pauses in speech and understand how to pause in a sentence. When teaching grammar, one thing I do is to have children talk and ask other children to transcribe their words. They listen for pauses and try and pick up a flow of conversation, editing out that which doesn't make sense and elaborating where necessary so that their writing becomes immediate. Another thing I'll do is have my students E-Nun-Ci-Ate in an exaggerated manner, painfully pronouncing each word, each syllable. Why? If I am correct about the sound of a language being important, then pronunciation will help students become aware of exactly what they are saying as opposed to what they think they are saying. It also slows them down and forces them to think about the logic of the sentences they are stringing together.
So do I teach writing or grammar? Depends on the group. Last year, I spent an eternity on helping students recognize and correct run on sentences. It was purgatory. Satan himself kept passing through, shaking his head sympathetically and offering to usher off some of the students. When Satan pities a teacher, that teacher really really deserves to be pitied. However, this answers the above question regarding grammar: is it important for a student to learn the difference between past perfect and future perfect, etc? No. Is it important the student knows what makes a proper sentence and be able to construct a complex sentence, perhaps with parallel construction? Yes. I don't care if they don't know how to label what they are doing, as long as they do it correctly.
Some writers who ask me to read their work will ask that I ignore the grammar and just concentrate on what they are trying to say. I respond to this with a dull look. I drool a little, too. Some writers have perfect grammar, yet their work goes nowhere. I still drool.
I drool a lot. It actually has nothing to do with my "people" skills. I just enjoy drooling.