Is it supported by Islam to request a religious exemption from the vaccine mandate in america based on the fact that aborted fetal cell lines were used in the development of the vaccines?

I understand your concern. However, from an Islamic perspective, it would not be haram to use such a vaccine even if if they used fetal cells in researching it. By using the vaccine you are not supporting abortion in any way, and society does not regard you as supporting abortion. Hence, it would be permissible to get the vaccine. Vaccine companies don’t advocate for abortions. They simply research fetuses that would be aborted anyway. So getting their vaccine would not be regarded as supporting abortion. Furthermore, if not getting vaccinated puts you at a serious risk (meaning you are convinced of this) then you are required to protect yourself and your health.