What is the general term for any person or persons who will be reading your writing?

The general term for any person or persons who will be reading your writing is audience.

Other terms you could use include:

* Reader(s)

* Target audience

* Intended audience

* Consumer(s) (if your writing is marketing-related)

* Viewers (if your writing is for visual content)

* Listener(s) (if your writing is for audio content)

The best term to use will depend on the specific context of your writing.