Extreme proponents of this "no mention of dead people" position sometimes use the adjectives "ghoulish" and "morbid", believing that any gesture would give the event funereal overtones and would shift the focus of the event.
Again, it is probably best to focus on the deceased's role along with other family members rather than to have a separate toast to that person alone. For example, an orphan might arrange for a toast to his/her extended family, including a reference to the deceased parents. This allows the guests to toast the living and the departed together, perhaps also thinking about future generations of the family as well.