When does an ideology becomes a religion or just philosophy or a way of living? Does each has any specific definition? or it depends upon person to person perception?
Buddhism is not ideology, not religion, not philosophy and not even a way of life.
Instead, Buddhism is a methodology that ends suffering & problems.
In MN 29, while Buddhism is described as the 'holy way of life', it is made clear this way of life has one goal & purpose, namely, 'the unshakeable freedom of mind'.
Such a methodology becomes ideology, religion &/or philosophy when it is not practised and therefore the results of its practise are not understood.
In addition, it becomes ideology, religion &/or philosophy when it starts to emphasise ideas such as reincarnation, which serve certain mutual worldly interests of monks & laypeople.
An "ideology" is a system of ideas (on any topic, but often used in the context of "political ideology"). Buddhism is an ideology, but it's more than just an ideology: e.g. Dhammadhatu said it's also a "methodology".
I think an essential characteristic of "religion" is obligation (e.g. "you are obliged to pray because God commands you to"). Buddhism can seem like or be interpreted as a religion (e.g. "you are obliged to believe and to accept, to have faith in, everything that's written in the suttas"). But some people don't interpret it like that, and might instead say something like, "I accept (only) what makes sense to me", or "I choose to practice this or that for my benefit", instead of seeing it as obligation i.e. as a religion.
I don't know how to define philosophy or way of living ... with my background I might also be inclined to call it a science, which is a form of knowledge.
This comment said, "I wish it was made clearer to people that Buddhism is NOT a religion or philosophy, but actually the antidote to being enthralled by those".