Live theater in the His Dark Materials universe must be wild. Surely an actor's daemon also has lines to recite, so their daemon's form probably also factors into casting decisions. Maybe some plays have vague character descriptions for daemons, but I bet other plays have really specific or central daemon characters. And sure, big-budget theaters can afford to hire a separate actor with a particular daemon to stand backstage while their daemon plays its part onstage, but community theaters don't have those kinds of resources.
Like if you're casting for Julius Caesar, surely the real historical Caesar had a pretty iconic daemon, right? Are you going to cast an actor with a pigeon daemon as Caesar and just have everyone suspend their disbelief that it's Caesar's lioness, ἁμαρτία?
Usually a human and their daemon are both actors. They are often loud and flashy - auditions are ways for both halves to show off their skills. This is the most common arrangement -- after all, acting is a calling that asks for your heart and your soul.
But sometimes it's just the human or, even more rarely, just the daemon who acts. A human auditions with another person's daemon as their scene partner, a charisma test like you do for a romantic pair. Their own daemon sits curled in a pocket or tastefully out of sight, often in the company of the other daemon's human.
Playwrights don't shy away from writing in daemon touching. After all, it's an evocative tool, another way to characterize without words. The glib-tongued man who lies to everyone whose daemon sits next to him, never quite touching. A composed woman whose daemon sits elegantly on her shoulder in quiet reassurance. Separated lovers who cling to themselves as they cannot hold each other.
It's a well known tell for an audience: if the character and their daemon don't touch onstage, they are two separate actors. After all, who would violate the great taboo for a fiction? Who would allow someone else to touch their soul night after night for a story? But an audience must be generous. The set is no more a garden in Rome than Cesear and his daemon are the same soul, but you suspend your disbelief and when the human actor's hand hovers just above the head of the dog daemon's mane you let your imagination fill in the blanks.
It's a well known secret among actors: if a human and a daemon touch onstage, their respective other halves could very well be just out of sight. Taboos exist to be broken, and what better reason to do so than in the pursuit of art?
Julius Cesear buries his hands into his daemon's fur. Off stage, a golden haired man sits a decorous six inches apart from a parrot. He moves his head into the invisible touch. She flexes a talon into her perch. The audience roars.
Yes! You get it! Touching someone else's daemon is a taboo in the first place because it's intimate. (Also probably because some people have extremely fragile or extremely dangerous daemons--"don't touch" is the safest assumption). But if a loved one touches your daemon it's a delight. Conversely, if anyone were to touch your daemon nonconsenually, it would be revolting.
The Magisterium, an analog to the Catholic Church, is the most powerful political entity in Lyra's world. Do you think the Fantasy Catholic Church wants people doing anything so ecstatically pleasurable as giving the manifestation of each other's souls a scratch behind the ears?? Obviously not.
But surely there are other societies that weren't shaped so heavily by the Magisterium's influence, in which asking to touch someone else's daemon is a personal but not completely taboo gesture.
And when it comes specifically to theater, it's not like actors haven't been defying the wishes of the Catholic Church since forever.