Ordering low carb without being offensive

I’ll be visiting Japan for a few weeks and need to maintain a low carb diet. I’m not sure how common this type of diet is in Japan., and I don’t want to constrain myself to eating izakaya and convenience store meals. Given the pride that the chefs take in the quality/prep of their meals, I don’t want to waste the food by simply leaving it uneaten nor do I want to offend. When ordering in restaurants (e.g., no rice, noodles or bread), what is the best way to request no starch in a manner that won’t be weird or offensive or rude?

It's quite easy to not be offensive. Just say you have health issues, and try to book in advance so that the chef can be prepared.

But you need to be a little more specific. In other words, the restaurant will ask you specific questions. Can you not take any starch at all or can you take a little? What can you take? Or what do you usually eat?

Also, if it indeed affects your health, make sure you have specific requests written down in Japanese and have it proofread by someone you can rely on such as a hotel concierge or a flight attendant to say the least.

By the way, I think it will be harder to maintain a certain diet through "eating izakaya and convenience store meals" because what they serve are usually the most unhealthiest of meals in terms of containing too much salt, fat and sugar.

Soba is made from buckwheat and about half the carbs from other white flour made noodles. Stay away from rice. Low carb done.

At some restaurant especially family restaurant, you can always order just the dish 単品 tan-pin, without the accompany rice etc.

It depends on what kind of restaurant and what food you order, but you can do it without offending anybody. Japanese are familiar with low carb diet.

For example, if you go into a sushi bar and don't want to eat any rice, then order sashimi (and definitely do not order a nigiri and just eat the fish on the top - that will get yourself kicked out). And don't go to a ramen shop and order a bowl of ramen without the noodle. But if you order a teishoku (meal set which usually includes soup, rice, entre, vegetable) but don't want the rice, you can specify "no rice".

Japanese are familiar with low carb diet.

We are? Is this the same thing as 炭水化物ダイエット that some locals follow to lose weight by obtaining starch but not whole bowls of it?

If so, I have the impression that most locals who follow this diet do eat a certain amount of carbs per day to maintain their health, such as a small bowl of rice per day or a bowl of udon per day.

Another thing is that a lot of Japanese course meals (tei-shoku) are designed to taste right when eaten together with plain rice. In other words, the non-rice dishes are often too salty to be eaten without the rice.

Perhaps it's best to ask if your orders are not too "salty (shi-o-karai)". And if you want to experience the saltier dishes, you may want to ask for "gohan sukuna-me (smaller portion of rice)" to go with it.

Most restaurants offer set meals from a menu and generally that will include carbs – rice, noodles, tempura batter, etc. Generally you can order `o-mori` (extra large serving of rice/noodles) but some restaurants will respect an order of `han-rice` - han meaning half. I rarely eat any rice after ordering han-rice, but instead it gets slipped into a small plastic bag and used separately, or disposed of. Some meals may offer a choice of bread or rice, which would allow you to feed the pigeons.

Many restaurants will offer `tanpin` (single dish) items – including salads, fried/broiled fish, etc.

Also, if you stay at a hotel where the meal is included, you may fare better as they may try to accommodate more, vs the production-line approach of restaurants. And if you stay where a buffet is offered, you can pick and choose to suit yourself.

Good luck…

Low carb diet (or let's say protein rich diet) is relatively popular in Japan. There is even a line of protein rich snacks at some convenience stores for those people following it. (I think it is called RIZAP)
As long as you choose dishes that are by itself low carb and likely high protein, you should be fine. It is to some extend a misconception that Japanese eats loads of rice. They do, but specially in restaurants, rice is just one relatively small part and you can simply say that you do not want it.
Obviously if you'd order sushi and then leave the rice part uneaten, that would be awkward, or ramen and you don't eat the noodles. But the same goes if you'd go to an Italian restaurant in your country, order a plate of spaghetti and then eat only the sauce. So just by ordering the kind of dishes that are good for you, you should be fine.
As a PP said, if it is an allergy bring a note in Japanese to specifically ask that it is not included. If it is "just" for diet, if there are some carbs on what you ordered, you could just ignore them.

Thanks to all for your advice and information. Very helpful and very much appreciated!