Besides being called as "cold-blooded mass murderer" and "racist", Che Guevara has been also labelled as homophobic. He has been said to discriminate homosexuals and put them into "concentration camps".
This is possibly the least researched territory in Che's life and in Cuban history, but let's try to find out the truth again.

The macho Cuban society was strongly homophobic and the Revolution did nothing to fight against the discrimination – even though from the 1970s a slow progress started and today the homosexual, lesbian and transgender people enjoy the same rights as the heterosexual citizens.
Homosexuality was considered as decadency and a learned behaviour, therefore researches were done to discover how to prevent it. Electroshock therapy and hormone treatment were also used (inspired by a Czech researcher, Kurt Freund). The revolutionary government enforced several anti-homosexual laws and a lot of homosexual men were sent to the UMAP camps.

Fact: Che Guevara never talked about homosexuality or homosexual people - at least not in public. No reliable source has been found about it.
I have found only one reference to a homosexual person, in his Notas de Viaje (Motorcycle Diaries), where he wrote about a man who had been beaten up by some people: "The episode upset us a little because the poor man, apart from being homosexual and a first-rate bore, had been very nice to us..." Possibly, for a macho man like Che, homosexuality was something strange and unattractive, yet it is not a proof of homophobia.
Fact: There is no proof of Che Guevara's discriminating homosexuals - or defending them.
Fact: Che Guevara had nothing to do with the UMAP. The camps were opened after his leaving for the Congo.

Let's talk about UMAP camps a little - that have been considered as "Cuba's concentration camps, more cruel than the Nazi ones" by certain Western countries.

UMAP (Unidad Militar de Ayuda a la Producción - Military Units to Aid Production) is the name of the camps that were established in Cuba in the province of Camagüey between November 1965 and July 1968.
In these camps, according to different sources, about 25,000 or 35,000 people were kept whom the government considered as "anti-social" or "counter-revolutionary elements" for example homosexuals, religious people and priests (Catholics, Protestants, Jehovah's Witnesses), non-comformists and intellectuals (writers, singers). However, not all the homosexual or religious people were sent to the UMAP - only those who were unwilling to act as committed revolutionaries.
Agricultural work (picking vegetables and fruit, weeding, or harvesting sugar cane) was used to "re-educate" these people - they were arrested, transported to Camagüey, then forced to work on the fields - spending their free time in the camp without electricity or running water. They had a day off every week, and after a period of time they could visit the nearby towns or even Havana, and they could meet their family members either near the camp or in their home.
Physical abuse was frequent, especially in the case of Jehovah's Witnesses, and there were people who even committed suicide - however, the most vital function of the UMAP camps were not violence or torture, but re-education and exploiting workforce.
Raúl Castro, the minister of the FAR (Fuerzas Armadas Revolucionarias - Armed Revolutionary Forces) is considered to have proposed the idea of UMAP camps, while the official newspaper Granma published an article in April 1966 stating that a group of military officials gave the idea to Fidel Castro.
After the protests of the Union of Cuban Writers and Artists (Unión de Escritores y Artistas de Cuba), international organisations and well-known intellectuals outside Cuba, the UMAP camps were closed.

We have no reliable source about what Che Guevara thought of homosexuals. However, we are given a story that shows that even though he was not religious and he wasn't keen on religions or their representatives (like most Communists), he was still ready to return a favour for a friend in need.

Let me quote from an article (Source #4):
"Seventh Day Adventists had a unique relationship with the Revolution and represent a very different relationship with the UMAP than other religious minorities. In 1956, there were nearly 5,000 Seventh Day Adventists in Cuba, with more than half located on the more rural, eastern end of the island. Oriente, the province where Castro began his uprising, was also the province with the most Seventh Day Adventists. In Oriente, one family of Adventists gave food and shelter to a band of revolutionaries who were fighting dictator Fulgencio Batista. Seeing that one of the men had no shirt because he had used it as a bandage to protect a wound, the father of the household, Argelio Rosabal, gave the revolutionary his only shirt. That wounded revolutionary – Ernesto “Che” Guevara – was so moved by the man’s generosity that Che promised them the construction of a chapel in the future (which was indeed constructed).
In December of 1958, Antillian College, a school ran by Seventh Day Adventists, fed and took care of wounded soldiers who were fighting in the Sierra Maestra. When the first draft for the SMO (Servicio Militar Obligatorio - Obligatory Military Service) was enacted, 70 of the 110 eligible students at Antillian College were drafted. After asking the government to release some of their students so that the school could function, the majority of the recruited Adventists returned to school. Still, the SMO was problematic for Seventh Day Adventists because it did not make a distinction between combatants and non-combatants. In response, the Seventh Day Adventist Church created a commission to write a memorandum asking the government to exempt the remaining 12 Adventists who had been called for SMO. The memorandum explained the distinction between serving combatant vs. non-combatant roles, Adventists’ unique Sabbath observance, and their loyalty to the government. The commission chose four pastors to deliver the memorandum along with one lay member, Argelio Rosabal – the same man who had sacrificed his only shirt to Che Guevara in the Sierra Maestra. Rosabal personally delivered the memorandum to Che, who on October 28, 1963, sent a letter enclosed with said memorandum to the head of the Agrarian Reform program, Carlos Rodríguez. In the letter, Che wrote, “[Argelio Rosabal] is the Adventist I spoke to you about … you will know how to evade the law, or how to divert my attention” . Che Guevara interceded on behalf of his Adventist friend, Rosabal, for an exception to be created in the SMO for this sect.
Later, it ended up that Adventists would be sent to the UMAP camps, but sociologist Caleb Rosado stresses that they were sent to the UMAP “simply … because [they] refused to bear arms [and] there was no other place to locate them” and not because they were considered lacra social, as the government regarded other UMAP internees." The Adventists received better treatment than other people.

Sources:

~ Source #1: Miriam Celaya, Dimas Castellanos - Cuba, page 474.
~ Source #2
~ Source #3
~ Source #4