Here’s the thing, though. It’s not a “non-verbal statement”. There is – explicitly! – a statement of belief in the reception of the Eucharist at a Catholic liturgy! The priest (or EMHC) says "
The Body of Christ" and the communicant responds “Amen” – which means “It is so.” In other words, the communicant explicitly affirms that he believes that this is truly the Body of Christ when he receives the Eucharist.
When I’ve explained it to non-Catholic Christians, I stress that, if they believe that this is truly the sacramental presence of Christ in the Eucharist, then reception of the Eucharist is an affirmation of that belief. And, since I don’t want to be the facilitator of having them lie in public (‘thou shalt not bear false witness’, remember?

), then I ask that they refrain from receiving the Eucharist. (And, depending on how well I know them, I ask them, if on the other hand, they
do think it’s really Christ, truly present in the Eucharist, then they’re really Catholic… and shouldn’t they want to leave their denomination and join our Church?!

)
I’ve heard a famous Catholic scholar use a different analogy. Let’s suppose that you have a marriage that’s rather… a-hem… ‘open’ in a particular way

. But, you have friends who don’t practice that sort of thing. When you’re invited to their house for dinner, would you walk up to your friend’s wife and plant a big kiss on her, and try to take her upstairs? Of course not! Even though it’s not your belief, you wouldn’t impose your beliefs on them while at their house – you’d honor their belief, and be a polite guest! Same thing here…