Is a woman who exercises at home sinful for continuing to watch videos of openly homosexual trainers, knowing that there are no equally competent alternatives and that there are no inappropriate behaviors in the videos?

It is not forbidden to benefit from training videos merely because the trainer is homosexual, as long as they do not contain anything Islamically prohibited. The basic principle concerning things is permissibility, and "Halal is what Allah has made lawful in His Book, and Haram is what Allah has made unlawful in His Book, and what He has remained silent about, He has pardoned." However, seeing corrupt individuals might negatively affect the soul, so it is better to achieve the purpose through another means if possible.