Eclecticism in the Dhamma (as per AN 3.72; AN 3.65; MN 20)

In Canki Sutta Buddha explained that people should not rely on tradition:

"Bharadvaja, first you went by conviction. Now you speak of unbroken tradition. There are five things that can turn out in two ways in the here-&-now. Which five?

1. Conviction,
2. liking,
3. unbroken tradition,
4. reasoning by analogy,
5. & an agreement through pondering views.

These are the five things that can turn out in two ways in the here-&-now. Now some things are firmly held in conviction and yet vain, empty, & false. Some things are not firmly held in conviction, and yet they are genuine, factual, & unmistaken. Some things are well-liked... truly an unbroken tradition... well-reasoned... Some things are well-pondered and yet vain, empty, & false. Some things are not well-pondered, and yet they are genuine, factual, & unmistaken. In these cases it isn't proper for a knowledgeable person who safeguards the truth to come to a definite conclusion, 'Only this is true; anything else is worthless."

..."If a person has conviction, his statement, 'This is my conviction,' safeguards the truth. But he doesn't yet come to the definite conclusion

Also note, when you say "Theravadin tradition", who is that?

Is there a person on the Earth who can speak on behalf of "Theravadin tradition"?

Clinging to "canon" is a bad habit of many people who claim to follow "Theravadin tradition". But there is no written rule that in "Theravadin tradition" you must have such bad habit.

However, better read and understand Canki Sutta rather than trying to follow tradition (which would be already a mistake Buddha advised against).

In Mahaparinibbana Sutta he said:

"Therefore, Ananda, be islands unto yourselves, refuges unto yourselves, seeking no external refuge; with the Dhamma as your island, the Dhamma as your refuge, seeking no other refuge.

Buddhists use the term dhamma in two main meanings:

1. phenomena (what is real),
2. teaching about what is real, or natural laws of something (e.g. "dhamma of awakening" etc.).

Thus I understand Buddha's advice as: do not rely on others or on texts; they wouldn't practice in stead of you. Take refuge in what is real and in your own practice.

The Pali suttas say there is only one path to Nibbana.

273. Of all the paths the Eightfold Path is the best; of all the truths the Four Noble Truths are the best; of all things passionlessness is the best: of men the Seeing One (the Buddha) is the best.

274. This is the only path; there is none other for the purification of insight.

Dhammapada

Does this verse imply that the Theravadin tradition is sticking too much on traditional teaching, and are unwilling to accept other approaches as well? Rarely do I see monks for example, who acknowledge other approaches who aim at the removal of grees, hatred and delusion.

Interestingly the adherence to traditional teaching is the factor that allows Theravadins to have an open mind. If one "sticks too much to traditional teaching", s/he'd have already studied and practiced the Buddha's teaching in AN 8.53:

Gotami, the qualities of which you may know, 'These qualities lead to passion, not to dispassion; to being fettered, not to being unfettered; to accumulating, not to shedding; to self-aggrandizement, not to modesty; to discontent, not to contentment; to entanglement, not to seclusion; to laziness, not to aroused persistence; to being burdensome, not to being unburdensome': You may categorically hold, 'This is not the Dhamma, this is not the Vinaya, this is not the Teacher's instruction.'

"As for the qualities of which you may know, 'These qualities lead to dispassion, not to passion; to being unfettered, not to being fettered; to shedding, not to accumulating; to modesty, not to self-aggrandizement; to contentment, not to discontent; to seclusion, not to entanglement; to aroused persistence, not to laziness; to being unburdensome, not to being burdensome': You may categorically hold, 'This is the Dhamma, this is the Vinaya, this is the Teacher's instruction.'"