I could have worded it more clearly, that's for sure (maybe an extra hyphen would've done it), but by "non-muslim theocracy" I didn't mean to say a theocracy of a different religion, just a country which isn't a muslim theocracy. I do know Uganda isn't nominally a theocracy, and that American evangelists were busy at work incensing the already existing local homophobic sentiments.
It looks like we were both wrong regarding the legal status of homosexuality in Uganda: a previous bill from 2014 was struck down by the Supreme Court in 2015, but last year Museveni signed the current bill into law. There's been at least one prosecution for "aggravated homosexuality" so far, but the "defendant" managed to get the charges downgraded and was freed on bail.
The point still stands that, of the 12 countries that punish homosexuality by death, 11 are muslim majority, and only one is christian majority.
Of the 55 countries that criminalise homosexuality, but do not punish it by death, 39 (77%) are muslim majority.
Of the 49 total muslim majority countries, only 10 don't specifically criminalise homosexuality. But, in a few of these, like Egypt and Jordan, LGB people are routinely persecuted under the guise of anti-prostitution laws or other statutes.
In many non-muslim majority countries, the muslim population is more hostile towards LGB people than the national average, as is the case in the UK, where 52% of muslims apparently want for homosexuality to be outlawed.
There is, of course, plenty of religious homophobia that is not of muslim origin. I don't think any major religion isn't homophobic (or misogynistic, or many other things), and I don't think I argued that. But, at least in the present, there is one religion that is noticeably more militant about it. Wouldn't you agree?
PS. Accurate statistics are very hard to come by. I've seen several sources describe Palestine / Gaza as a state where homosexuality is legal, for instance. But I don't think it affects the larger picture.
Edit: auto-correct typos!