Personally, I believe the world would be vastly different. To sum up my main points;
For example, religion keeps cultural evolution in check. Without a religion to keep the Western world united, the cultural difference between the Western countries would be much larger, and as such, likely lead to more wars.
As for homosexuality, it used to be widely accepted. In Rome, males were considered "for pleasure", while women were considered "for family". The bathhouses were unhygienic due to all the men having sex with each other. The bathhouses had a special room where you get naked and oil up. Usually, you went through various discussions, mostly political or business. Occasionally, they had sex. In Japan, homosexuality were widely spread amongst the Samurai ranks. When a young male became a full-fledged Samurai, one of the older members would introduce him to the adult world by having sex with him. Homosexuality weren't really considered bad in the Western world until Christianity arrived and deemed it bad.
While women would likely be considered the weaker gender without religion, my opinions are rather split here. Throughout various nature tribes with the typical shaman/animalistic religion, the women stay home and take care of household work. Yet, these women consider themselves very happy. Having several wives is natural, not because it is considered powerful, but because it eases the work load on the other women. Having only one wife take care of the kettle and household work is too much, and as such, they marry several women to make it easier on them. Additionally, the women are not necessarily the ones raising the children, the older children are. Despite women doing the "lighter" handiwork, they are still rather equal. However, in today's society, it would be considered sexist. So it depends entirely on what you consider to be sexist and how far you take it.
Religion has had a huge impact on science, especially Christianity where it were considered blasphemous to speak about any views other than religion. However, the Mayan religion were, for example, almost entirely built around science and the understanding of nature. As such, I believe religion can have both a good and a bad influence on religion, depending on how the religion itself is writ. That being said, without religion it is likely mankind would still pursue the understanding of nature, so I believe without religion science would be more advanced today.
Despite what a lot of religious people I've talked to seem to think, religion did not write our morals. We know instinctively that killing innocent people is wrong, and no one like having people stealing from them. However, without religion, it is likely that each country would have a varying set of laws and morals. While we might know stealing is wrong, it is something religion likely has taught us to be wrong. Our strongest instinct is our so-called baby voice, which is the part of our instinctual system that is egoistic. We strive to make it better for ourselves all the time, and taking things from others while defending our own stuff is part of this. For example, small children has a tendency to take toys from other children, because that's what their instincts tell them to do. They don't know this to be wrong, until we teach them. If there is no religion to teach people stealing is wrong, I don't consider it too unlikely that the concept of stealing being wrong to have never been invited. However, the last part is not entirely true, as it conflicts with another very strong instinct we have;
Self preservation. The fear of being rejected is, together with egoism, one of our strongest instincts. Being rejected actually activates the same part of the brain as physical pain. Stealing things as food (while it can be beneficial), can have horrendous consequences to human survival. If caught, can lead to the rest of the rejection. Humans are group animals, and as such, being rejected from the group can lead to death.
This is a short write-up of some my views on the topic, I hope I can get some input on them.
Also, Khajit, Christianity changed the Roman empire greatly. From Christians being hunted and killed, it was now the official religion. While as a start is simply meant Christians were no longer hunted and killed (the Roman empire had a high tolerance for religion at this point, as a great number of soldiers had varying believes such as Mithra and other ancient Roman religions), it eventually lead to the church forbidding all other religions and starting a witch hunt on non-believers. To be honest, I would say Christianity is one of the reasons the Roman empire eventually fell, as it divided the empire.