We have a young Baptist couple who are very good friends and neighbors. We enjoy them and their children very much and are frequent guests in their home. They are aware that we are Objectivists and that we do not share their beliefs. They never proselytize. We expect and accept that there will be long narrative prayers before meals when we are their guests, but it is somewhat unsettling when they bring this verbal prayer practice into our home when they are our guests. Is this an ethical question or simply an issue of etiquette. Are we wrong to say nothing and just accept this?
The question describes the neighbor-friends as follows:
They are aware that we are Objectivists and that we do not share their beliefs.
This is a very good start. However, a "belief system" inevitably has consequences (or needs to) sooner or later, or else it's just empty "hot air." The prayer ritual is such a consequence. The questioner should consider what would happen if the questioner were to talk to the other lady alone and quietly sometime, in advance of another visit to the questioner's home, to find out if the other family would be willing to suspend their ritual while visiting the questioner's home. If the questioner must respect the other family's customs while in the other family's home, then some degree of the reverse ought to be understandable and reasonable, too, when they visit the questioner's home.
If that is unacceptable to the other family, then perhaps, if they truly understand that Objectivists do not share their beliefs, they would be willing to accept a ritual on the part of the Objectivists, whereby the Objectivists remain standing during the prayer, perhaps standing behind their chairs, leaving the chairs pushed in at the table and their heads upright, until the prayer ritual is finished. The questioner could consider doing that in the neighbor's home, too. The questioner could simply explain that it is her family's own symbolism in support of reason (and rejection of mysticism), which is as important to the pro-reason family as its opposite may be for the other family's religious affiliations.
One might call this "symbolic etiquette," but some form of expressing the real difference between an Objectivist perspective and mysticism is likely to become essential sooner or later anyway, to make sure there is no possible confusion about where Objectivists stand on mysticism. If the other family comes to regard this as an unacceptable influence on their children, then perhaps the mealtime visits to each others' homes should end.
I can't recall ever being in this specific situation myself; at the very least, I would certainly decline to bow my head or show any indication of participating in the prayer ritual, probably leaving at least one hand visible on the table instead of in my lap where it might be assumed that I had my hands clasped together, as in prayer. Even that much may not be enough if the ritual involves "long narrative prayers" rather than some kind of quick and simple saying of "grace." I have been in churches from time to time for weddings or memorial services for someone who died. At the very least, I have declined to bow my own head or clasp my hands during the prayer rituals. No one has visibly complained to me about it.
The questioner could also consider adding a brief "grace" of sorts for her own family after the "long narrative prayers" are finished, something acknowledging the values of reason, purpose and self-esteem and the connection between food on the table and human productiveness. Not in the form of a prayer, of course.
The question states that the young Baptist couple "are very good friends and neighbors. We enjoy them and their children very much and are frequent guests in their home." One has to wonder how much value one can really derive over time from people who insist on rituals of "long narrative prayers" before meals, even when visiting others' homes, including the homes of known Objectivists to whom such rituals might be an uncomfortable, anti-rational sight. If the neighbors truly have rational values to offer to Objectivists, they ought to be able to understand the need for at least a little adjustment when in the homes of Objectivists or sharing meals with anyone who sees great value in reason and a great conflict between reason and mysticism.
The question also states: "They never proselytize." But any show of resistance to the "long narrative prayers" may provoke proselyzing sooner or later. If so, one wonders what value the friendship would still be able to offer, a point on which the questioner seems to agree. Expecting atheists to sit idly by and say nothing to challenge mysticism while others pray is a form of intimidating non-believers. The non-believers should find an appropriate way to shrug off the intimidation, visibly so (or curtail or terminate the relationship).