From the 1920s onward, when vaccinations were being promoted but the public were nervous, if not skeptical about this comparatively new form of preventative medicine, there were a great deal of negative comments published by a whole raft of different groups, not all of them Christian ones. But, over time, as vaccinations proved their worth (despite there always being a few bad results with some individuals) the public began to trust them more. The negative comments lessened and nowadays the issue of whether Christians should, or should not get vaccinated has almost ceased to be a religious issue. It is a matter of individual conscience, except in a few groups where leaders let it be known (to their flocks) that they think it is wrong, and they discourage them. Where congregation members let their leaders do their thinking for them, they accept their leaders' arguments and suppose that they are, indeed, promoting a biblical stance against vaccinations. We see a bit of this in America in some small Protestant groups, where they are refusing to be vaccinated against Covid-19.
Please note, however, that some reasons have nothing to do with Christian faith, but are based on the right to refuse medical treatments, according to individual conscience. More than a few people object to what is increasingly looking like government blackmail - not allowing people to certain large public events unless they can prove that they have been fully inoculated against Covid-19. It is also involving air travel passengers.
One example that showed religious reasoning in the 1920s and 30s, but which no longer prevails, is in the following quotes. But let me stress at the outset, that this group no longer holds these views. Individuals in the group are free to decide for themselves now. Back in the 1920s and 30s, however, the religious principle invoked was based on their belief that they should not take any blood into their own veins. The view was that vaccination caused animal blood cells to be injected into humans, and that was equated with eating blood. Here are the relevant quotes for that:
"Vaccination never prevented anything and never will, and is the most
barbarous practice... We are in the last days; and the devil is slowly
losing his hold, making a strenuous effort meanwhile to do all the
damage he can, and to his credit can such evils be placed... Use your
rights as American citizens to forever abolish the devilish practice
"The public is not generally aware of how large an industry is the
manufacture of serums, anti-toxins and vaccines, or that big business
controls the whole industry... the boards of heath endeavor to start
an epidemic of smallpox, diphtheria, or typhoid that they may reap a
golden harvest by inoculating an unthinking community for the very
purpose of disposing of this manufactured filth."
"Thinking people would rather have smallpox than vaccination, because
the latter sows seeds of syphilis, cancers, eczema, erysipelas,
scrofula, consumption, even leprosy and many other loathsome
affections. Hence the practice of vaccinations is a crime, an outrage,
and a delusion."
"Vaccination is a direct violation of the everlasting covenant that
God made with Noah after the flood."
"As vaccination is a direct injection of animal matter in the blood
stream, vaccination is a direct violation of the law of Jehovah God."
Quotes from The Golden Age magazine, from 1921 to 1935, particularly
Feb. 4, 1931 issue, page 293.
By the late 1980s all of that had long stopped, and more neutral comments were made in The Awake! magazine (which replaced The Golden Age). For example, in the 22 June 1990 issue, page 28 merely reported statistics about the phenomenal success of the global smallpox vaccination campaign. It added that the World Health Organization held a few vials of the virus, but made no comment (nor any reference to the publisher's earlier stance, as quoted above!)
There are many factors involved in public reluctance to accept vaccinations. Ignorance at the outset is usually replaced, in time, with understanding of the many benefits, so that harmful results are viewed by the majority of the public as a lesser risk than not being vaccinated. If Christians state they have religious grounds for refusing, they may quote their religious leaders, or say it is a matter of individual Christian conscience. But some of the religious reasons given in the 1920s and 30s no longer get a mention because they are clearly just plain wrong.