Nothing stops you hitting Cancel if you don't want to deal with the new SMS right away.

This is how my old Palm did it. Upon receiving an SMS, a dialog popped up with the sender's details, the SMS text and Reply, Cancel and Delete buttons. Reply would bring you to the communication thread with that sender. Cancel and Delete closed the dialog and returned to whatever you were doing before. Not pressing anything until the screen timed out meant the dialog was still there the next time you turned the screen on. Receiving another SMS while an unaswered dialog was on the screen would change the dialog to something like "2 messages received". Obviously the senders' details, SMS text and the Reply button were no longer applicable and disappeared.

I found this interface the most intuitive of all phones I have ever used, before or since, but of course YMMV. For me, SMS is the most important method of communication with a mobile phone and the reason for having a mobile phone in the first place.