Freedom to Go 'n Grow Together in Christ
For ISIS, throwing homosexuals from a "high place" is currently the preferred method of execution for homosexuality.
If the victim is unfortunate enough to survive the fall, then stoning is required to finish the job.
If you wish to know more concerning ISIS and homosexuals, see ISIS Murder of Homosexuals: Incidents of LGBT Executions in Islamic State.
(08/24/2016) ISIS Tosses Four More Gay Men from Top of Mosul Building. More news from the "religion of peace." Where are the vast masses of "moderate Muslims" condemning this? I'm sure there are some, but ....
In Iran, the preferred punishment is hanging. It is unclear how many homosexuals are executed in Iran (and other Muslim countries). In some cases, crimes may be listed with vague names such as "immoral behavior."
Homosexuals Under Islam
When it comes to women (see Women Under Islam), Islamic websites (those written by Muslims or on their behalf) go to great lengths to describe how well women are treated under Islam. Women are "equal" and "precious" and they are "jewels." There is no such pretense regarding homosexuals. Homosexual acts are not merely considered sinful, they are crimes. The most common punishment is death, although under some schools of Sharia Law, the punishment for a first offense is "merely" a severe beating. The next offense merits death. The punishment can sometimes be less severe: life imprisonment, 100 lashes (which may result in death), and the like.
Clearly, homosexuality is treated in extreme fashion in the Muslim world. Islam, in theory, distinguishes between homosexual acts (a crime) and homosexual thoughts (not a crime). But Muhammad himself criticized both, declaring that homosexuals should be killed, and cursing effeminate men, saying they should be turned out of their houses. It is difficult to imagine that ISIS or any other extreme Muslim authority is going to make much of an effort to distinguish between "doing as Lot's people" and merely being "effeminate."
So while Islamic websites and Islamic scholars in general make little or no effort to whitewash Islam's treatment of homosexuals, that does not mean that there are no apologists for such treatment. The apologists' primary approach is to blame Islam's punishment of homosexuals either on "Napoleonic Code" or "Victorian attitudes" adopted by the ruling elite. That is, the West is to blame. I've had people blame "honor killings" on the same. Given that honor killings and Islam's treatment of homosexuals predate the 19th century by over a millennium, such arguments are specious.
For a good, relatively brief overview, see Islam and Homosexuality at WikiIslam.
There are currently 10 countries where the official penalty for homosexuality is death. These countries are: Iran, Iraq, Mauritania, Nigeria, Qatar, Saudi Arabia, Somalia, Sudan, United Arab Emirates and Yemen. For more details, see this article from the Washington Post. Although they are not "countries," ISIS, the Taliban and Al Qaeda are similar. In many other countries, homosexuality is a crime. The punishment varies from trivial to severe. Countries with severe punishments tend to be, but are not uniquely, Muslim majority.
For more on legal punishments for homosexuality, see 7 Worst Capital Punishments for Being (Illegally) Gay. The title is incorrect as the article includes non-capital punishments as well.
For a good article comparing Islam and Christianity, how each treats homosexuals, and the Scriptural basis for each, see Sharia sure ain’t gay from Answering Islam (a great, general purpose website about Islam).
May I summarize? Homosexuals should all beat a hasty retreat from Islam and any countries dominated by Islam. While women should be doing the same, they are rarely risking their lives if they do not.