openmw.org

Is there a mod to reduce the voiced greetings and it is compatible with OpenMW?
It feels so immersion-breaking that just walking around one start yelling at the player "No, I don't think so," and similar.

This one requires MWSE, so it won't do. (Right?)

correct.

Try https://www.nexusmods.com/morrowind/mods/43994

All it does is change one GMST, iGreetDistanceMultiplier .

Morrowind Mod Maker Manual v2.pdf wrote: Used for those annoying voice greetings NPCs use when you get too close
Specifically (if the construction set help is to be believed) this is multiplied by
their hello rating to get the distance before they talk.

By default it's set to 6, the mod changes it to 4.
I have reduced it to 2 on my openmw install.

That manual has lots of info, it can be downloaded from http://lovkullen.net/Emma/edvardmd.htm