Which indicator, that there are unread posts, is the one you want to overcome?
The slightly different text color in the topic list, the number of new replies next to a topic, or the topics appearing in /unread?
I think the second and third only happen when the notification status of the topic is “tracking” or “watching”. You could prevent the status from being changed when your users open the topic by changing the default other auto track topics after msecs site setting to never. If you don’t want the status to change after they reply, you can also adjust the default other notification level when replying setting.