What Donald Trump received was a cocktail of two monoclonal antibodies. There are various ways to produce those, Regeneron does state on their homepage that they use Cell Lines for mass production. This does not mean stem cells, there are many cell lines that are not stem cells.
For research the antibodies are produced in mice, Regeneron calls their system for this VelocImmune.
I couldn't find a direct statement on which cell line they use on their homepage. But in an article in Science I finally found a direct statement that the antibodies are produced in Chinese hamster ovary cells:
The monoclonal antibodies from the two companies are clones of potent
SARS-CoV-2 antibodies that can “neutralize” the virus in test tube
studies. Researchers plucked the genes for these antibodies from
humans who recovered from COVID-19 or from mice artificially infected
with the virus. The companies then put the genes in Chinese hamster
ovary cells to bulk manufacture the antibodies, which were given to
the COVID-19 patients as infusions.
Chinese hamster ovary cells are not stem cells and neither are they human. No fetal tissue nor fetal stem cells were involved in the actual production of the antibodies.
There is one aspect of the development, but not production, of the antibodies where a cell line derived from fetal tissue was used. To generate a target that looks like SARS-CoV2 they used HEK293 cells. Essentially they modified a virus called VSV to contain the Spike protein from SARS-CoV2, and to mass-produce that modified virus they used HEK293 cells:
HEK 293 cells were generated in 1973 by transfection of cultures of normal human embryonic kidney cells with sheared adenovirus 5 DNA in Alex van der Eb's laboratory in Leiden, the Netherlands. The cells were obtained from a single, apparently healthy, legally aborted fetus under Dutch law; the identity of the parents and the reason for the abortion are unknown. Wikipedia
The HEK293 cell line was derived from a single aborted fetus (HEK = Human Embryonic Kidney). Cell lines are immortal, so all HEK293 cells in use in various laboratories all around the world are derived from that single first cell.
There are many different cell lines, another example are the CHO cells that were used to produce the actual antibodies that were originally derived from hamster ovaries.
HEK293 cells would not have been the only choice for these experiments. I found a paper describing similar experiments with a modified VSV that tested several cell lines for producing the modified VSV. You can see in figure 2 that they used Huh7, 293T, Hep3B, PLC/PRF/5, HepG2, HeLa, Vero and BHK. You can clearly see that the different cell lines were not all suited to the task, 293T was one of the best but the Huh7 cell line was a tiny bit better.
So strictly speaking, for one experiment designed to test how well the antibodies bind to the virus a cell line originally derived from fetal tissue was used. But stricter versions of this claim like e.g. that the research would not have been possible without fetal tissue are not supported in my opinion.
