Though, would the post still appear for all the people who follow me? Since in that case I'd want only the ones who "agreed" to this to be able to see.

That depends on their settings, if you mean the feeds those are entirely separate, going to your posts page will still show all of your tweets like normal, the feeds would be to make a gallery page, those who know to pin feeds and use those instead will do so and you can inform people to do so.