How best for a Christian to explore the ethics of a Covid-19 vaccine that might use farmed cell-lines from aborted foetuses? I looked through the CMF website at their Briefing paper When demand outstrips supply: A Christian view of the ethics of healthcare resource allocation during the COVID-19 pandemic:

“The British Medical Association (BMA) has recently produced guidance
around the ethical issues presented by the COVID-19pandemic.8 NICE has
also produced a rapid guideline for adult critical care during the
pandemic, which includes guidance for decision-making around
escalation. 9 In addition, the Royal College of Physicians (RCP) has
issued guidance, in conjunction with other stakeholders such as the
General Medical Council, the Faculty of Intensive Care Medicine, the
Intensive Care Society, royal colleges and faculties.10 As Christian
doctors, we must consider how we can respond to the ethical challenges
posed. Here we will attempt to consider some of the issues involved,
and how to think about them biblically, using Beauchamp and Childress’
widely recognised four pillars of medical ethics11 as a framework.”

However, it must be too soon for a briefing paper on whether any of the current seven Covid-19 vaccinations produced have utilised cell-lines from aborted foetuses. The matter of demand for vaccines was not included.  Then I looked at a tagged blog, posted 20 November 2020, which sounded promising, COVID-19 vaccines: the wider ethical questions for Christians. Alas, no mention was made of the ethical issue I wish to explore.
Some success came via a contact working professionally in the realms of Christian ethics. He sent a pdf of an article written by a colleague of his in a Catholic journal, Anscombe Bioethics Centre – Friends’ Newsletter, Summer 2020, Issue 47. (His link to the pdf will not open when I copy it.)
Dr Helen Watt, Senior Research Fellow of the Anscombe Bioethics Centre, wrote the article, pp 9-12.

“… Vaccines are normally, though not always,4 produced in living
cells. While they can be generated (as with some COVID-19 vaccines in
the making) in cells derived from ethically uncontentious sources such
as insects,5 tobacco plants,6 and hamster ovaries,7 they can also be
produced in cell-lines made from tissue derived from an aborted unborn
child. One such cell-line used in COVID-19 vaccine research (including
a project of the University of Oxford8 ) is the HEK 293 cell-line
modified from tissue taken from the kidney of an unborn child aborted
probably in 1972, while another is the PER C6 cell-line from the
retinal tissue of an 18-week baby aborted in 1985.”

I wish to know both ethical considerations involved and how to identify which Covid-19 vaccinations might have such ethically questionable ‘ingredients’. I will not go to popular media outlets for this as a huge amount of disinformation is being bandied around. This question is addressed to Christians who have ethical compunctions against any use of aborted foetuses, which transcends denomination. I note this  related question indicates deep concern but I seek to know how to find out if that's being used with some vaccines.
Edit:  this question become more important since the Church has now made a statement regarding the newest vaccine from Johnson and Johnson.  See this
This is a matter of conscience, quite clearly.
I well know how these matters may be viewed by the ungodly as I was disciplined in a certain company many years ago (final written warning on the first instance of its occurrence) because of this very issue arising, suddenly, without my being prepared to meet it and I reacted in a way which was unacceptable to the management.
However in this case I wonder if the words of Paul are not relevant :

... asking no question for conscience sake: [1 Corinthians 10:25 KJV]

In the situation the apostle speaks of, one wishes food and wishes to buy it in a market but its origin is unknown. It could have been previously offered to an idol and one would not want to partake of that, but that is only one of a variety of possibilities.
Paul advises not to delve into origins for the sake of conscience. He advises to accept what is being traded at face value and not to make the enquiry.
In our current situation, what is being offered to us is not - principally, in a way of being an absolute necessity of its development and function - fundamentally dependent on the issue that has been here raised.
Certain cell lines have been incorporated into general medical research. A prime example is that of Henrietta Lacks' (1920-1951) cancer cells which became the HeLa line of cells and have been enormously productive, medically speaking, and her memory is now being properly recognised.
It may be that other cells, which in the past have been taken from a source that I would prefer they had not been, have been incorporated into the various research lines which are part of an established data base of genetics.
But as far as I know, the origin of those cell lines is not a fundamental necessity to the development of the product. The cells could have been from anywhere.
The efficacy of the product is not dependent on that issue for its success, is what I am emphasising.
To me, in this particular case, I feel it not necessary for me to make elaborate enquiries in order to free my conscience from any burden. I am content with the words of the apostle, in this instance.
When I was offered treatment by a dentist to strengthen the bone in my jaw, it was he who mentioned that 'donor' tissue (from a cadaver) could be used and I declined and he said he could use proprietary collagen instead.
Once I was injected and no longer aware of my surroundings, he could, for the sake of his own convenience, have used cadaver tissue in my jaw. But I do not feel the necessity to further interrogate him and to demand that he prove to me what he did or did not do. I stated my conscience and I have left it at that.
Looking back with hindsight, I could probably have avoided a final written warning over the matter of a supposed 'abortion' being the source of a sample I was testing, and looking back, it now becomes clear that someone knew my sensitivity and was merely trying to provoke me over it. But I later took voluntary redundancy and got a very generous termination package (thank you to all concerned) and I now reap the reward of a useful pension from the company.
I hope that this helps in the present situation.

I am a Licentiate of the Royal Society of Chemistry (1978) and was given further private training in Molecular Biochemistry when I worked in the Pharmaceutical Industry making products which incorporated radioactive isotopes (for medical research purposes and for cancer treatment).