Why wasn't Bohemian Rhapsody given a China release?

Well, Bohemian Rhapsody got a limited release in China. It released on March 22, 2019

According to The New York Times, the Queen biopic hit theaters in the country last weekend, but it was an altered version that omitted references to lead singer Freddie Mercury’s sexuality. Per the Times, those references include the scene where Mercury, who was bisexual, discusses his sexuality with his fiancée, and the scene that introduces Mercury’s future partner, Jim Hutton.

It is difficult to pin down why was it not being released in China -- as mentioned in the comments -- maybe because gay themes are not well received in China. Homosexual activity is banned from TV in China.

An interesting thing would be to know why it got released. Probable reason for release - an economic one according to this

Chinese media regulators began limiting actors' salaries last year, capping their pay at 40% of production costs. Lead actors can't be paid more than 70% of total cast pay. The country's biggest movie star, Fan Bingbing, also disappeared from the public eye for three months in 2018 after she was accused of tax evasion as part of a crackdown on secret contracts. She publicly apologized to the Chinese government in October.

In the midst of this crackdown, China approved more Hollywood movies for release in December in an effort to reach its box-office goal of $8.7 billion by the end of 2018. While box-office growth slowed to 9% compared to 13.5% growth in 2017, it still passed its goal and reached $8.87 billion.

This media climate could be a factor in why China has approved "Bohemian Rhapsody," a global box-office hit, for release. China is projected to pass the US as the world's box-office leader within the next five years

The film did okay business there, by grossing close to 14 million dollars.

Edit:

I thought it would be worthy to explore a bit more about the release of the film in China and discovered the how of the release. The film was imported into China by the National Alliance of Arthouse Cinemas (NAAC). But, the alliance only has around 3700 participating screens out of China's 60,000 screens.

So far, only five of the films have been imports: Oscar winners “Manchester by the Sea” and “Three Billboards” from the U.S., “Nise: The Heart of Madness” from Brazil, Hirokazu Kore-eda’s legal thriller “The Third Murder” from Japan and now “Bohemian Rhapsody.”

And, the alliance is exempt of the quota system:

Alliance films still go through a rigorous censorship process but don’t fall prey to China’s quota system, which limits the country to just 34 titles a year from abroad. Foreign titles brought in through the NAAC can be shown only in participating cinemas,

But, the alliance too is wary of showing gay themed films -- and they regard Bohemian Rhapsody a film about music.

The Freddie Mercury biopic might seem an unlikely choice because of its LGBT content, since the NAAC had previously described to Variety a policy of not working with such films. (Scenes of men kissing and dressed in drag, as well as the word “gay,” were cut.) However, the alliance said it did not regard the movie as gay-oriented but rather about music.

Perhaps, what can be more important about this release, is that in Bohemian Rhapsody we are witnessing a Trojan Horse entering China.