The proper way to whisk matcha is with a bamboo chasen, because the many-stranded-ness promotes a frothy result.
But bamboo doesn't fare well in a dishwasher, and it isn't clear if a trip through the dishwasher would serve to sanitize bamboo anyway.
So do foodservice venues that serve matcha use a stainless steel whisk instead? Is there anything about stainless steel which reacts with the matcha and detracts from it somehow?
You seem to be confusing several things here.
First, about sanitization: it's a synonym for disinfection. It means to treat items and surfaces with chemicals which kill bacteria directly, e.g. with bleach. It isn't the same thing as cleaning, and is an additional step done after the cleaning.
Sanitization is only required by food safety regulation in some specific circumstances. For example, a restaurant might be required to sanitize the food preparation surfaces (counters) at regular intervals. It's not prescribed for utensils for food preparation, or for cutlery with which the food is served - not for knives, not for forks, not for matcha whisks. These get cleaned.
Also, the dishwasher doesn't sanitize the items put into it. It washes them, and is merely an automation of the process of washing by hand. The point of washing is to remove any food residue that might become the breeding ground for a bacterial colony. For that, you need warm soapy water which dissolves the sticky parts of the food, and mechanical action, which removes the dirty water and larger pieces of food. Manual washing is just as good at that as a dishwasher, frequently even better, if you do it properly. It's just unpopular because manual labor is more expensive than dishwashing machines.
A matcha whisk is also easier to clean than some other items. Since it doesn't come in contact with fat (which needs soap to dissolve) or animal products (which are typically contaminated with more pathogenic species), and the matcha isn't especially sticky, you could in principle just rinse it instead of washing it with soap and a sponge. I don't know if this is allowed by regulations though.
Also, don't fall into the trap of thinking that your cutlery is somehow sterilized. This isn't the case if you wash it manually, if you put it through the dishwasher, or even if you sanitize it. The last one will kill the bacteria present on it, but it will be immediately re-contaminated with bacteria from the environment. And that's OK. You're in constant contact with bacteria, and your body knows how to deal with this. The point is to not have a spoon covered in several grams of gravy sit around for days, and then eating with it without washing it, introducing billions of bacteria (and the excretion products in their colony) into your mouth, as opposed to the few dozens present on a washed spoon.
So the above explains why your assumption (that a dishwasher-safe whisk is required) is incorrect. From there on, the question "why use a bamboo whisk" becomes a business decision made by the restaurant owner, and addressing that part is off topic here. But I hope I made it clear that a bamboo whisk is a perfectly viable option, not in any way prohibited by safety regulations.
I have researched further about matcha and how bamboo matcha whisks (Japanese: chasen) are used. @rumtscho 's point about matcha being low in fat is a useful point.
Matcha is literally ground up tea leaves. The matcha-poweder particles do not themselves dissolve, although chemicals in the particles do leach into the water in solution. A nutritional analysis (USDA) gives 100g of matcha as having 0g fat and 0g sugar). It is alkaline (pH of 9 or so), and its 'microorganic achilles heel' is mould.
Not cleaning the bamboo whisk well (where cleaning is understood as removing loose clumps and particles of matcha adhering to the surface of the bamboo) is the invitation to mould.
However, a bamboo which which has been cleaned and dried is not going to attract any mould, and from a food-safety perspective, could be considered not to harbour harmful microorganisms.
As to the point that bamboo is porus and will probably soak up some matcha-solution, it doesn't matter provided the bamboo is able to later dry. Best-practice with whisking matcha is to soak the whisk in hot water before use (to make the bamboo tines more pliant and less prone to snapping during the mechanical action of whisking). So it is wet, slippery bamboo, swollen with water to restrict the size of the pores, which comes into contact with the matcha paste, and is therefore less likely to trap the comparatively large particles of matcha. Pigmentation from the matcha solution still has a chance to soak in, but microorganisms probably don't want to eat that. Finally, best practice cleans, rinses and dries the whisk immediately after use, further reducing the likelihood of mould.
Sanitization can be accomplished either by chemical means (eg. the caustic chlorine-based 'detergent' in the dishwasher, or alcohol, or ammonia) -OR- by the application of sufficient heat for a sufficiently long period. In food-safety, sanitization does not refer to sterilization, but merely to good odds of killing a sufficient number of bugs to give ordinary immune systems an easily conquered small dose of pathogens.
While caustic chemicals in the dishwasher are no friend of bamboo, bamboo can cope just fine with the '80-degC for 2 minutes' ... or thereabouts ... required by most food-safety regulators. So immersing a cleaned whisk in sufficiently hot water for a sufficiently long time is an acceptable sanitization technique.
But is it necessary to sanitize the whisk in-between each drink that is prepared? I would think not, since - barring contamination from other substances in its environment while being used - the lead-time for mould to gather in pathogenic numbers on a cleaned-but-not-sanitized whisk is likely more than a single day.
Thus, food safety can be accomplished by: