Is Mahasi Sayadaw's "counterfeit dhamma"?

The true teaching attributed to the Buddha is found in the Tripitaka. So it is best to sticking with this orthodoxy than innovate with other practices. This way your practice is closest that the Buddha taught. The Buddha being more accomplished than anybody else and also having the quality "Leader of persons to be tamed" would have preached the best mode of practice to follow.

It is always good to be orthodox as dhamma disappears when counterfeit Dhamma emerges:

Kassapa, the true Dhamma does not disappear so long as a counterfeit of the true Dhamma has not arisen in the world. But when a counterfeit of the true Dhamma arises in the world, then the true Dhamma disappears. - sn16.13

Also discussed in more detail in this answer.

Like there are Christian, Muslim and Hindu are Buddhist countries. There are Buddhist countries also how has a history, culture and tradition of trying to preserve the Dhamma. This will make people of a Buddhist cultural upbringing be protective of the doctrine (pariyatti), practice (patipatti) and the fruit (pativedha) for future generation. Culturally some may feel this as a duty when brought up in a Buddhist environment.

In addition, regardless of the label you add as X tradition or Y tradition or A religion or B religion the Dhamma is universal and works the same way as long as you practice the right way. There is only one right way (ekayana magga) which is what is given in the Maha Satipatthana / Satipatthana Suttas. The Buddha gives a guarantee that you will get results of the practice this the right way. The key here is you should practice it in the way prescribed in the Sutta to get the results. To get the result you have to reconcile you practice with the Sutta and do accordingly. Applying a label as this is the technique of X tradition or Y tradition or this teacher or that teacher does not decide the results. It is the correct practice which gives result. If you are not getting results you should recheck what you are doing to see if it confirms to the steps given in the prescribed method to which the guarantee by the Buddha is attached to. This is more analogous to going through the instruction manual properly before assembling something. If you do not follow the instruction what you assemble will not work. If you follow it then it will work. Also if you do not follow the instruction manual properly the warranty also maybe void. Having said this one is one's own master, hence anybody is free to follow what they wish.

The question had the following also which since seems to be edited away.

Why are Mahasi Sayadaw's teachings controversial? Can you outline the arguments which people present, in favour of and against these teachings?

For this please refer to this answer and linked content.

"Or he might say: 'Whereas some recluses and brahmins, while living on the food offered by the faithful, engage in wrangling argumentation, (saying to one another): "You don't understand this doctrine and discipline. I am the one who understands this doctrine and discipline." — "How can you understand this doctrine and discipline?" — "You're practising the wrong way. I'm practising the right way." — "I'm being consistent. You're inconsistent." — "What should have been said first you said last, what should have been said last you said first." — "What you took so long to think out has been confuted." — "Your doctrine has been refuted. You're defeated. Go, try to save your doctrine, or disentangle yourself now if you can" — the recluse Gotama abstains from such wrangling argumentation." Brahmajala Sutta

Is generally my fallback option for argumentative encounters within Buddhism.. There was a sutta in the MN where the Buddha asked a few of his top disciples about how they perceive the Dhamma, and they all gave somewhat different answers, but the Buddha was happy with all of them (if anyone knows the one, thanks in advance!).

I guess in the end this is to do with where one draws the line between concepts and practices deemed to be of absolute necessity for progress within the path, and concepts and practices that are deemed useful, but may be adjusted based on personal experience. (Khandhaka 5 for the Buddha allowing monks variance with regards to rules and practice in Avanti, a place closer to modern day Mumbai than Nepal)

Concentrating on the diaphragm rather than the nostrils is detail and arguably not worth discord.. Buddhism, more than any other practical philosophy, is an individual path and people come to it from different angles. It is well defined overall, but concentrating on the differences between one's own practice and another's is avoiding the fact that to progress one needs to concentrate on one's own practice. There is room for analysis and advice, and any point should be analysed according to merit (beginning of DN1 again). I would however say that if a statement doesn't sit within right speech, it becomes harder to take it as coming from an authority within the Buddhist sphere.