The problem seems (as usual) to be stated in the initial false presupposition.
I am aware that the verb think can be used in the progressive form in some contexts,
but it cannot be used in the progressive when someone is expressing one's opinion.
I have no idea where this comes from, but it sounds like something a teacher might improvise on the spur of the moment when they couldn't answer a student's question. In some schools, this would then be passed on as
The Correct Answer for the next ten generations. It's not a grammatical rule of English, however.
Pretty much any predicate can be used in the Progressive construction, if the speaker wants to indicate that whatever state or activity the predicate describes is not over yet at the time referred to.
In English, optional constructions like Passive or Progressive don't change the basic meaning of the sentence, but they do guide the interpretation of the predicates. Think can express an action, or it can express a state of mind. Mental process verbs are odd that way -- all mental process is imaginary, after all, so we can imagine it any way we please, as stative or active.
When the Progressive is used, however, it simply means that whatever thinking is being referred to is not instantaneous, as either state or action, but rather has an extension in time beyond the time the thinking is referred to. The thinker is not done thinking yet, in other words.
That's all, really, if you're only concerned with think. However, note that think is only one of many English mental process predicates, including emotion predicates and sense verbs, all of which have their own special unique grammars. Dictionaries are the wrong place to look for answers to grammatical questions; they deal with words, not constructions, but English grammar is all about constructions, not individual words.