When you say that the situation that you are in has become ‘intolerable’, what you are suggesting is that it has become unbearable; you find it extremely difficult to deal with. The word can be used with both people and things.
For example, when you say that the movie was intolerably boring, what you are suggesting is that you could not sit through it.
The word ‘intolerant’, on the other hand, is mostly used with people, and it is always used to show disapproval. Someone who is intolerant is very narrow minded; he is not very accepting. He is not willing to consider ideas or beliefs of others that are different from his own; he expects everyone to be like him. One is usually ‘intolerant of’ someone or something.
My grandmother is very intolerant of girls who wear jeans and t-shirt.
You’re our party leader. How can you be so intolerant of other people’s beliefs?
The constant criticism from his boss made Ravi’s life at work intolerable.
The pain from the wound was becoming intolerable.