Secondly, I'm certainly not a foody but I am an Australian. Shouldn't it be Tasmanian Pepper not Tazmanian Pepper? I know that your description does match the Menu, but it doesn't sound right at all. Taswegians are very proud of their food, and I wouldn't want to make them angry.
Unless, of course, it was Pepper from the early 90s Sega Mega Drive game Taz-Mania, based on Taz the Tasmanian Devil. If that is the case, I'll happily withdraw my comment!
As far as allergies, guests are asked when reserving if there are any allergies in advance. I would presume that the chefs would make dramatic changes to the menu to adjust for allergies if known in advance (peanuts and celiac the most common these days).
When it comes to specific guest dislikes, I've never experienced a situation where I came across something I didn't think I would like. My guess is that the chef would ommit the ingredient, substitute another ingredient, or put that ingredient off to the side of the plate, but still pursuade you to try it. There's a possibility that another dish from the standard menu may get substituted if the chef is unable to perform an ingredient elimination or substitution. Most fine dining restaurants purchase ingredients daily, often with the Chef's Table Menu in mind, so it's unlikely for a kitchen to be able to stray far from what ingredients they happen to have on hand. Additionally, some chefs may be uncomfortable creating a brand new dish on the fly without testing it first, so you're likely to get a spin on a standard menu item or perhaps a dish from a recent Chef's Table menu.
Ultimately, most guests who choose to do a chef's table experience are interested in the culinary journey, and should be open to trying lots of new things.