Rav Ovadiah zt”l says, “Talking in a shul or beis medrash (during tefillah) delays the Geulah.”
He bring it down in the Yabe’ah Omer 1:10:11. I don't know what what 1:10:11 stands for. Can someone send me a direct link of where this is located?
Moreh Mikdash brings the following in the name of the Zohar Parshas Achrei Mos. There are 3 things that lengthen our time in Galus. One of them is "She'osim Kolon B'shechina B'galus". The Zohar in Parshas Teruma says that one who speaks in Shul is "Gorem Kolon L'shechina". Thus one who talks in Shul vain talk is lengthening the Galus.
Mainstream Halacha (Rambam, Shulchan Aruch and similar) clearly forbids talking during certain parts of the prayer service - like during the Amida.
Other times they permit talking under certain circumstances - like during Shma if one needs to answer a person one fears.
Other times talking is technically permitted. If
talking in a shul or beis medrash (during tefillah) delays the Geulah, then surely the Poskim would have mentioned this - at least as a Chumra or a good idea.
Furthermore, one could argue that not ever talking during tefillah delays the Geulah. Sometimes being friendly to a newcomer, or helping a person with a problem, or passing on relevant - timely - information is a Mitzva of "Love your fellow Jew".
Often people don't understand (nor appreciate) mimes, especially when they're trying to concentrate in praying. A few well chosen words are often worth a thousand hand signals.
The Geula is being delayed - IIRC - because of Sinat Chinam - which is the flip side of VeAhavta leRe'acha. So not talking in shul may sometimes delay the Geula.
That said, as DoubleAA already pointed out, needless talking in a shul or beis medrash is often a sign of disrespect for the place, and any sin could potentially delay the geula. Especially since a shul or beis medrash is a Mikdash Me'at - and if we don't respect those, we can hadly be worthy of the rebuilding of the real Mikdash.