Would I be in a difficult situation if I asked the barber to change the channel to a Quranic channel or a religious lecture while someone else is having his beard trimmed in the same place?

There is no harm in requesting to change the channel to one that broadcasts the Holy Quran or beneficial lectures, and this is what is required when one is able. There is no accountability for the presence of someone shaving their beard during that time. Coming to this place is permissible and not sinful, and one should denounce evil according to their ability.