I've looked in the settings and can't find anything about it. If it bothers you that much you can download a 3d party messaging app like Go SMS or Handecent. I never though about it until I read your post. It's strange that there wouldn't be a setting to turn that off.
Kind of a backwards way -- but would it work if you disable notifications in stock messaging but use light flow to assign a color and a sound? I would try it right now but it's midnight and I don't think anyone is in the mood to text me back haha.
I just tried it and nothing. The screen still comes on. I had a Nexus 4 before I got the S5 and the native Android messaging app actually had a setting to either have the screen come on or not.
Kind of a backwards way -- but would it work if you disable notifications in stock messaging but use light flow to assign a color and a sound? I would try it right now but it's midnight and I don't think anyone is in the mood to text me back haha.
My screen doesn't light up when i get a text, I've selected to show on lock screen but nothing happens. I still recieve texts and text sounds but that's it.
Related question: If you receive a text and don't touch the phone the screen turns off, this is ok, however the LED notification light is not on. If I go settings -> display -> LED indicator the notifications option is ticked.
Missed call does exactly the same - no LED indicator.
It's because the galaxy s6 and some others use their own text messenger instead of the base android one(and theyou disguise it to look like the android one). just search Messenger and look for the one made by google.