I wonder if them approving will effect the religious mandate exception

I think it's important to keep in mind this letter was written during the tenure of Pope John Paul II and Eminence Cardinal Joseph Ratzinger, who would go on to become Pope Benedict XVI. Both were staunchly opposed to abortion. In fact. Pope Benedict criticized Biden's pro abortion agenda in March 2021. As far as the position of the Catholic Church stated in the letter, it isn't as simple as vaccines derived from aborted fetuses are ok when there isn't an alternative. According to the letter, the only time the use of a vaccine derived from aborted fetuses it's morally acceptable for Catholics is in extreme circumstances when (1) there isn't alternative vaccine AND (2) it's to stop the spread of a pathological agent that poses an existential health threat to yourself or others OR (3) the vaccine is compulsory. Considering there are sucessful treatments for COVID that don't derive from an aborted fetus and the COVID survival rate and consistent with the Church's position stated in the letter, Catholics are morally obligated to make a conscientious objection to the COVID vaccines. The only exception would be for those who COVID poses an existential threat to their health.