Is it permissible to study under a sheikh who has a trimmed beard and an elongated garment (thawb musbil), knowing that he is accused of belonging to the Muslim Brotherhood, and does studying under him constitute an endorsement of his ways?

The questioner should be keen to benefit from the aforementioned Tajweed teacher, because learning Tajweed is a good thing. The fact that the teacher makes mistakes does not prevent this; for an error in some particulars, from which no one but the infallible is free, does not justify abandoning benefiting from the one who errs. Rather, what should be abandoned is imitating him in what he has done incorrectly.