"I think that we cannot make an exception."
Translation:Pienso que no podemos hacer una excepción.
At first, I too thought subjunctive. However, recently I watched a podcast that the subjunctive is used when we say: No pienso que... The same goes for: No creo que... In the affirmative we do not use the subjunctive. These are two of those all too familiar exceptions we find while learning Spanish.
I reported that "No pienso que podamos hacer una excepción." should be a valid answer, too. I do not see any difference of the meaning.
You are incorrect. The indicative is used with creer que and pensar que, while the subjunctive is used with no creer que and no pensar que.
Because it is saying I think (pienso/pensar) that we cannot make an exception, not I believe (creo/creer) we cannot...
Is it wrong to use me parece instead of pienso as far as expressing your degree of belief?
The phrases "creo que" and "pienso que" are fairly interchangeable, like "I believe that..." and "I think that..." in English. But the most literal translation of "I think that..." is "Pienso que", of course.