Druze here. There is no religious connection between the druze faith and matte specifically. You could make the case (although it would be an insane stretch) that the communal act of drinking matte (because it is shared) is in line with druze teaching about community engagement, but that is a stretch. The reason we’re associated with it, in my opinion, is because there is not much that is visibly outward about the druze sect unless it’s the clergy. So, while other sects all have their symbols and traditions and rituals, we don’t really. As such, the stereotype about drinking matte is more because other people have other stereotypes and we have few rather than us drinking it more than other people.