Can a Christian take vaccines that contain aborted fetal cells?
No vaccine contains fetal cells.
Viral vaccines require cells to replicate viral information. There are three types being used today: egg-based, cell-based, and recombinant. In the first two methods, actual natural viruses are used. In recombinant, a synthetic virus created and then introduced into cells for replication.
The cells used for replication are called Madin-Darby Canine Kidney Cells (or MDCK) [https://www.cdc.gov/flu/prevent/cell-based.htm]. As the name implies, the cells were originally isolated from the kidney cells of two dogs, names Madin and Darby, back in 1960 [https://en.wikipedia.org/wiki/Madin-Darby_Canine_Kidney_cells].
After the viruses are grown, they are isolated from their growing medium and then inactivated.
There are other vaccines, however, that do use human cells that were originally gained from two aborted children back in the 1970s and 1980s. Like the MDCK cells, these cells are continually reproduced in a cell bank. No new cells have been collected over the years. The vaccines that use human cells to replicate the disease are chickenpox, shingles, rubella (mumps), and Hepatitis A [https://www.verywellhealth.com/do-vaccines-contain-aborted-fetal-tissue-260337]. Like the viral vaccines, after the disease is grown, it is isolated from the cells to create the vaccine.
Some of the vaccines being developed for COVID-19 are being grown using human cell lines originally obtained from aborted children, but others are using other cells [https://www.sciencemag.org/news/2020/06/abortion-opponents-protest-covid-19-vaccines-use-fetal-cells]. The article cited lists the five vaccines that used human cells from aborted children. In particular, the two current vaccines about to be approved from Pfizer and Moderna are not produced with human cells [https://www.health.nd.gov/sites/www/files/documents/COVID%20Vaccine%20Page/COVID-19%20Vaccine%20Fetal%20Cell%20Handout.pdf].
As a Christian, I oppose the killing of children. Thus, how the cell-lines were originally obtained was ethically wrong. Thus, the guilt for what was done falls on the originators. They should have found a way to harvest the needed cells without harming a child. When the time comes that new cell-lines need to be established, it should be insisted that it cannot be done from an aborted child. But as it currently stands no additional cells from aborted children have been used in the United States.