This is an interesting Maxim in that it is one of the few that specifically seems to look at behavior in a religious context. In a ceremonial setting we are active participants, but as there are few of us in the modern era a relatively large percentage of us have “speaking” parts in that we recite (and sometimes even sing) the hymns honoring the Gods and the prayers that are being said. But, this Maxim instructs us to be respectful of the setting and not be disruptive by talking out of turn or by telling the person leading the ceremony that it is being “done wrong”. (Both of which I have had happen in ceremonies I have been part of.)
Being religiously silent means actively listening to what is going on and devoting our full attention to the service and honoring of the Gods. It means quieting our minds so that we can hear the voices of the Divine Ones speaking to us through the words and actions we are taking part in. And, most importantly, it is in being respectful of the need for others to be able to participate as fully as possible in the same way.