Complex sentence: In 2003, the Vienna Philharmonic appointed its first woman musician in 2003 after 161 years of operating without women, after removing the ban on women musicians in 1996, when it was threatened with budget cuts by the Austrian government.
Split into simpler sentences: In 2003, the Vienna Philharmonic appointed its first woman musician after 161 years of operating without women. In fact, there was an explicit ban on women musicians until 1996, when the Philharmonic was threatened with budget cuts by the Austrian government.