A woman's battle with leukemia has led her family to start a worldwide movement to get more people to sign up for stem cell donations — even earning an endorsement from famed author J.K. Rowling.

Please RT! A Eurasian donor is desperately needed to save this young woman's life. Do your thing, Twitter! https://t.co/oP24CINiOf — J.K. Rowling (@jk_rowling) January 11, 2016

But one barrier to getting more people on donation registries is homophobic restrictions on donations that persist around the world to this day.

The campaign, Match4Lara, is primarily about finding a matching stem cell donor for Lara Casalotti, a 24-year-old Chinese-Thai-Italian student in the UK, who was diagnosed with acute myeloid leukemia in December 2015. Doctors say she'll need a stem cell donation to survive.

The process for signing up to donate is, thankfully, very easy. It's as simple as spitting in a cup or tube, which lets lab technicians evaluate if you're a match and keep your information on hand to contact you for future donation needs.

What complicates Casalotti's situation is her mixed-race background, which makes it a lot more difficult for her to find an exact match. According to the campaign, about 3 percent of people on public stem cell registries are mixed-race. This makes it very hard to find a matching donor for someone of mixed background, especially since only a small portion of the population signs up for donations in the first place.

But there's another problem: government restrictions on who can donate, particularly men and transgender women who have sex with men. At the blog Wronging Rights, Kate Cronin-Furman explained:

Gay men are still restricted in their ability to donate blood products and bone marrow. In both Australia and New Zealand, any man who has had sex with another man in the previous 12 months may not donate blood or bone marrow. In the U.S., the U.K., and Canada gay men can donate bone marrow, but are still prohibited from giving blood if they are sexually active. The U.S. recently (last month, in fact) shifted from a lifetime ban to a 12 month deferment, a change the U.K. made in 2011. Canada, which currently requires 5 years of abstinence (!), will likely follow suit soon. These regulations are discriminatory and unnecessary. They categorize all sex between men as inherently risky, on par with intravenous drug use. And they don't just harm the dignity of gay men. Earlier this week, a friend of a friend tried, and failed, to register as a bone marrow donor in Australia. He's a gay man, of mixed Chinese and Italian heritage, who thought he might be a match for Lara.

These policies were established in the 1980s and '90s during the height of the HIV epidemic. Back then, there were a lot of fears and uncertainties about the transmission of HIV, with the disease originally believed by some to be related to sexual orientation. HIV blood tests were also much less effective, failing to detect the virus for months.

Today the situation is very different. We know much more about how HIV is transmitted, and that it's linked not to sexual orientation but to specific sexual acts. It's better understood that same-sex relationships can be and often are monogamous, which minimizes risky behavior. There are now nucleic acid tests that can detect the virus within weeks of exposure. Blood donations are regularly tested for HIV. And various studies found that less restrictive standards on donations don't negatively impact blood supplies.

But governments have been slow to adapt to the changing science, making it harder for people in need to find matching, lifesaving donors.

It's simple probability. Since such a small part of the population is mixed-race, and only a small portion of the overall population signs up for donations, it's always going to be a bit difficult to find a matching donor for someone of mixed background. And it's going to be even harder if the government sets dubious restrictions on who can donate.

Watch: How most states still discriminate against LGBTQ people