If a person has committed major sins that caused them to receive Bad-Dua (curses) from many people, then does Islam believe that the offspring of the person will also be affected by those curses regardless of how pious and righteous they may be?
No one will be responsible about the bad deeds of others unless he agrees with the sinner. Many well known sinners had very pious children and their pious children never been included in the curse on their parents. Allah (SWT) says in Quran ( That No one shall bear the burden of another) Sura 53, Verse 38.
Wassalam.