Obviously the nation state of Uganda didn't exist and even today its population is ethnically diverse, so take my 'Uganda' as a vague geographical term, rather than a political one.
Ugandans who are vocally against homosexuality often talk about it being incompatible "Ugandan values." A common counter argument to this in, say, India, is that homosexuality was criminalised by the British, not the indigenous population. Do we know whether this was the case in Uganda?
The Baganda people from Uganda were...and still are, a kingdom of several minor tribes located in present day Uganda. They were led by kings known as Kabakas.
At the advent of colonisation in the late 19th Century, the Kabaka then was known as Kabaka Mwanga II. He led a spirited fight against the British and managed to secure the interests of his people despite facing a stronger, better equipped enemy.
However, based on widespread allegations, Kabaka Mwanga II was gay...and oral history seems to have it his wasn't an isolated case.
That's about as much of Ugandan history as I can recall from my primary school education, and a quick online search. I hope the links help you get more information on the topic.
I am not an expert in African history, but I wrote the background section of the Wikipedia article titled Uganda Anti-Homosexuality Bill. It's kind of a disaster now, but here it is when I edited it last in 2012: https://en.wikipedia.org/w/index.php?title=Uganda_Anti-Homosexuality_Act,_2014&oldid=459711131
I used this source: Homosexuality in “Traditional” Sub-Saharan Africa and Contemporary South Africa (pdf here: http://semgai.free.fr/doc_et_pdf/africa_A4.pdf). As you can imagine, it is not about Uganda itself, but Sub Saharan Africa as a whole, and mentions several examples of male homosexuality. Similarly, when I wrote the Wikipedia article for Lesbian (here: https://en.wikipedia.org/w/index.php?title=Lesbian&oldid=488799834 see section titled "Africa"), I used sources to cite that lesbian relationships have been accepted in some places throughout Africa, but the concept of "lesbian", a woman who dates or partners with other women exclusively, has not. For example, what we might clearly define as lesbian sex in the West does not qualify as sex in Lesotho, because traditional notions of sex include the presence of a penis. See Aldrich, Robert, ed. (2006). Gay Life and Culture: A World History, Thames & Hudson, Ltd., pp. 237-238.