Avoiding talking in shul during davening (prayer services) is a difficult task and requires planning.
On an individual level one can a) go to a quick Hashkamah (early) minyan (service); b) daven (pray) in a shul where the Rabbi insists on no talking; c) choose a seat close to the front (Mizrach) and if all fails, step out of shul for a few minutes and do the talking outside.
At the shul level a) the Rabbi can insist on no talking; b) the Gabbi can keep the service moving along at a “good clip”. Our shul has replaced MiShebayruch’s (prayers for individuals getting called to the Torah accompanied with a pledge to the synagogue) with silent donations through pledge cards.