Do the COVID-19 vaccines use fetal tissue?

None of the 3 vaccines contain fetal tissue, per data presented in the CLI document regarding the 3 vaccines currently licensed in the USA, which appears accurate and consistent with other independent sources. Neither of the RNA vaccines are derived from aborted fetal cell lines, or use fetal cell lines in any phase of manufacture,  though a cell line derived from either a spontaneous or elective abortion in 1973 was used early in the research phase of these vaccines to evaluate efficacy. The Johnson and Johnson vaccine does use an adenovirus-infected fetal cell line derived from an elective abortion in 1985 in the manufacturing process.
Were the Pfizer and Moderna COVID-19 vaccines developed using fetal cell lines?
-The mRNA COVID-19 vaccines produced by Pfizer and Moderna do not require the use of any fetal cell cultures in order to manufacture (produce) the vaccine. Early in the development of mRNA vaccine technology, fetal cells were used for “proof of concept” (to demonstrate how a cell could take up mRNA and produce the SARS-CoV-2 spike protein) or to characterize the SARS-CoV-2 spike protein)
The Pfizer and Moderna vaccines were found to be ethically uncontroversial by the pro-life policy organization the Charlotte Lozier Institute. Further, the Secretariat of Pro-Life Activities, a committee within the United States Conference of Catholic Bishops, has stated: “neither Pfizer nor Moderna used an abortion-derived cell line in the development or production of the vaccine. However, such a cell line was used to test the efficacy of both vaccines. Thus, while neither vaccine is completely free from any use of abortion-derived cell lines, in these two cases the use is very remote from the initial evil of the abortion…one may receive any of the clinically recommended vaccines in good conscience with the assurance that reception of such vaccines does not involve immoral cooperation in abortion.”
When it comes to the COVID-19 vaccines currently approved for emergency use, neither the Pfizer nor Moderna vaccines used fetal cell lines during the development or production phases. (So, no fetal cell lines were used to manufacture the vaccine, and they are not inside the injection you receive from your doctor.) However, both companies used the fetal cell line HEK 293 in the confirmation phase to ensure the vaccines work. All HEK 293 cells are descended from tissue taken from a 1973 elective abortion that took place in the Netherlands. 
To make their virus vector vaccine, Johnson & Johnson infects PER.C6 fetal cell line cells with adenovirus. All PER.C6 cells used to manufacture the Johnson & Johnson vaccine are descended from tissue taken from a 1985 elective abortion that also took place in the Netherlands. They use this cell line because it is a well-studied industry standard for safe and reliable production of viral vector vaccines.
None of the COVID-19 vaccines in development use fetal cells taken from recent abortions. 
The Vatican has issued clear guidance that permits Roman Catholics in good faith to receive COVID-19 vaccines that use fetal cell lines in development or production. 
                Vatican: Without alternatives, current COVID-19 vaccines are morally acceptable - Catholic News Service