Perhaps you remember the controversy many years ago when it was disclosed that several vaccines in common use were derived using two cell lines, each from an electively aborted fetus. On the basis that receiving these vaccines would be cooperation with the evil of abortion, some Catholics wanted the Church to back their moral objections to being vaccinated for school or competitive sports. Vatican ethicists decided that since the dangers to children were grave without vaccine and that any cooperation in the two abortions (performed in the 1960's and 1971, legally in the Netherlands) was so remote, there was no morally compelling reason to refuse the vaccines. The responsibility to lobby for and use ethically derived vaccines, if available, was emphasized.
After abortion became legal in many Western countries, scientists speculated the rich harvest of fresh, healthy fetal tissue would yield bountiful medical benefits. As laboratory techniques and scientific knowledge advanced, the push for federal funding for human fetal cell research was on. In 2001 President George Bush banned federal dollars for research on newly created human fetal cells, limiting federal funding to studies using those cell lines already in existence. The following year, a national commission declared a moratorium on human cloning research in the United States.
When the race for COVID vaccines began, some bishops' conferences warned that the process should avoid use of the tainted cell lines. However, the two vaccines likely to be approved first did use the controversial cell lines in their development. This is the reason some are raising moral objections to these vaccines. Using the same reasoning as for the MMR and chicken pox vaccines, Vatican ethicists say their use is permitted.
Long answer: Due to the fact that the evil associated with the two abortions used in establishing these cell lines was remote and those who receive it neither want nor promote abortion, and considering the proportionate risks of non-vaccination to be grave both for the individual and those with whom he/she may come into contact, the vaccine may be taken. At the same time, we must do all we can to assure that future research techniques do not commodify human life. If and when a morally preferable vaccine becomes available, it should be used.
Short answer: No moral reason not to get vaccinated.