Because I have a much higher shot at being safe and living just fine there as a gay man vs a Muslim country? That is something I see as better.
It's generally safe to do so in North America (pre-Trump), West Europe, and Scandinavia. Certainly much safer than in Muslim countries.
It's true that secularism is what improved conditions for queer people and not Christianity but the thing is that Christian-dominated countries have achieved secularism on a wide scale. This is not seen in the muslim world. There's too much of a stronghold of religion on the people and the state there that won't wash away any time soon. There's too much outrage and religious zealotry that prevents progress from secularizing the state. This has happened in turkey to the most extent but that's about it.
Startpage works decently.