One answer is that your sister can't tell the difference between a "certified Naturopath"'s self-published blog and a scientific publication with editorial oversight and fact-checking.
Another answer is guilt by association. Some religions thrive on guilt; you'll often see religious people take guilt by association to an extreme. Some feel they can't bake a cake for gays, or listen to a prayer given by someone not of their religion, or let pro-choice politicians attend church services, because to do any of these things is to share in guilt by association.
Decades ago, scientists took tissue from one already-aborted fetus, and used it for research instead of throwing it into a fire. This research did not incentivize abortion in any way, and no fetal tissue remains in a finished vaccine. But again, some religions thrive on guilt and will take guilt by association to an extreme, and make stuff up if necessary to enforce that guilt.
For example, the naturopath claims in her blog, without citing a source:
We are talking about hundreds, if not thousands of aborted babies who have been and continue to be dissected in order to obtain the perfect cell line for the vaccines...
This is utterly false. The cell line from that single fetus developed decades ago, WI-38, is the same cell line in use today. Labs can use one copy of WI-38 cells to grow as many new copies as needed, and every copy will be identical and predictable. Tinkering with "hundreds, if not thousand" of new cell lines would inject enormous uncertainty into vaccine production for no benefit.
Finally, there is a compelling link between abortion and vaccines - but it has nothing to do with WI-38. Rubella in pregnant women can infect the fetus. Fetal infection with rubella can result in fetal death, necessitating either spontaneous abortion (miscarriage) or surgical abortion to remove the dead fetus. A single rubella outbreak in the U.S. in 1964-1965 led to 11,250 spontaneous or surgical abortions. (CDC) In other words, "vaccine-preventable abortion" isn't part of the standard pro-life vocabulary, but it should be.