I think there is a disconnect here on what it means to be a serious writer or to take your writing seriously.

Being a serious writer or taking your writing seriously does not have anything to do with the tone of your writing or whether you as a person are inclined to be serious or light-hearted. A serious writer can writer humor. A serious writer can be the class clown. You can be a serious writer and still only write on weekends. Taking your writing seriously means putting care and consideration into it.

Being a serious writer is the opposite of being a hobbyist or half-hearted writer, someone who does not put careful thought and consideration into their writing craft or writing business. But it also does not mean that you are anxious and stressed and overworked all the time.

Nor is taking your writing seriously the same thing as taking yourself seriously. It has nothing to do with ego or self-importance.

I am a serious writer. I take my writing seriously. I am disciplined, I put the time and effort into it. I love it. I enjoy it. I share it. I write stuff that is serious and stuff that is funny. I see nothing wrong with being a serious writer.

And as far as being cool goes... who knows. I've never been concerned with being cool. I think plenty of serious writers are cool, but cool is not what I'm striving for.