It's very important. It will be difficult, if not impossible, to be understood if you write answers and questions that have too many grammar and spelling mistakes.
You're right. It's bad form and it lowers the quality of the site if there are too many spelling and grammar mistakes, especially on the frontpage. It could turn off new users and affect the level of engagement in the site. A minor mistake here and there wouldn't make much of a difference. The goal, after all, is to be understood. But, if you have too many grammar mistakes, then it will be very difficult to get your point across and your answer or question will be misunderstood, if not completely ignored.
This is actually stated in Musing.io's curation guidelines. You can read it here: https://docs.google.com/document/d/1WKYGhdPhLKNHytsxAPPQiXyv5UBY6nUKM8IhG5PUgfA/edit
So, its a challenge for both the curators and users like us. I'm sure the curators have a way to filter the poorly written answers and questions. However, as users, it's up to us to make sure we do our best to write well-written answers and questions. And, at the very least, run whatever we write through a spell and grammar check before hitting the submit button.