Is there anywhere a halachic point of view that talking may be permitted, and that it does not have a negative affect on the tefilot?
Can members of a shul halachically stop people from talking? Can anyone provide any sources as to why you may be allowed to?
The Rambam (Hilchos Deos Perek 6:7) says that if one is told to be quiet and they rebuke the person telling them to be quiet they are subject to certain punishments including being barred from entering the Shul.
The Kaf Hachaim (Siman 151:8) says it is better for one not to come to Shul then to come and talk.
Mishna Berura (124:27) says every Shul should appoint a Mashgiach to punish those who talk during Shul.
Sometimes talking during davening or other times is okay but then it wouldn't be mundane speech it would be related to the mitzvah you are fulfilling.