In that case, we are all off the derech anyway so we shouldn’t care that Popa heroically pretends to be frum. And to people who literally never talk during davening, that is irrelevant and if you want to express it, do it in some manner that doesn’t respond to my point. But if you are a reasonable person, you understand that while it may be against halacha* to talk during davening, there are also other concerns with putting up a sign that says that people are not welcome in your shul. Be careful what you wish for, you just might get it.
*Also, be careful about making up halacha, which is arguably more assur than talking during shul. Almost all mention in halacha about talking during davening refers to talking during actual davening. Almost none of it talks about Kabbolas Shabbos.