The programme matches bone marrow donors and cord blood units with leukaemia patients and people with other illnesses.
The bill reauthorizes the National Marrow Donor Program for another five years.
Nick Dyer, a spokesman for Congresswoman Greene, told The Independent: “Nothing in this bill prevents the funding of aborted fetal tissue by taxpayers. It opens the door for the NIH to use this bill to research the remains of babies who were murdered in the womb.”
The sponsor of the bill, California Democrat Doris Matsui said in a statement that the programme provides the "only potential for a cure" for some individuals with fatal blood illnesses.
"For the 1.3 million Americans suffering from blood cancer and bone marrow disorders, we must continue to make investments in these programs that have saved tens of thousands of lives. I applaud my colleagues in the House for approving this bipartisan legislation and I urge the Senate to do the same," she said.
Asked why she voted against the bill, Lauren Boebert told The Independent: "This bill added hundreds of millions of dollars to the national debt, while not receiving a [Congressional Budget Office] score or going through the committee process.”
The bill states that “$31,009,000 for each of fiscal years 2022 through 2026” will be appropriated.
Rhode Island Democrat Jack Reed has put forward the law in the Senate and it’s currently being processed by the health, education, labour and pensions committee, according to Newsweek.
Two members from each party are sponsoring the bill in the Senate, indicating that it's highly likely to pass with bipartisan support.
According to The Leukemia & Lymphoma Society, someone in the US dies of blood cancer every nine minutes.
Twitter users slammed the two staunch conservatives, with one calling them "comically evil".
Prominent atheist Hemant Mehta wrote that "some people will do anything to reject science".