Why does it look like this sentence is using "but" twice in a row?
でも、 そうかと言って、 もう一つ下のレべルのクラスだと、 やさしすぎてつまらないと思いますよ。
To my knowledge, でも means "but". On the other hand, my textbook says the phrase "そうかと言って" also translates to "but, still".
Is the sentence being redundant here? If it's not, what kind of "feel" am I suppose to get from this sentence?
There is no redundancy in this sentence -- none. If redundancy existed, that would be because you translated word for word by using a dictionary.
It says 「でも、 そうかと[言]{い}って」; It does not say 「でも、しかし」, 「でも、それでも」 or 「しかし、それでも」, which would be redundant.
How about "But even if that were the case"?
「そうかと言って」 is used to state a contrary idea/opinion while partially admitting that there is some truth and/or validity in the other idea/opinion that has been presented.
It's not. Don't take the translation of そうかと言って so literally. This link here states 3 optional translations for the word. Could be translated as "nevertheless", "and yet", etc. It actually might not qualify (maybe someone else can chime in) but think of it as an idiomatic expression.
Also worth noting, in general, Japanese is far more forgiving about saying the same things twice in different. The more formal you get, the more common it becomes.
