Some people think or say that he is because they think he appears as a "girly" character compared to Snake, but it is clear that he isn't gay due to his female relations in MGS2. I think that a lot of people were just upset that only a few hours into the game, Snake leaves and here you have to play with this new character.
Raiden is not in MGS3, it takes place a long time before MGS1 and he wasn't introduced until MGS2. In MGS4, as far as Snake goes it ends kind of like MGS1, with him still infected with a Foxdie virus and not really knowing how long he has left. He finds out that he has a new Foxdie as well, that could possibly mutate and infect everybody, not just the people that it is designed to target. But they do defeat Ocelot/Liquid and bring down the Patriots and put an end to the whole thing, and he then learns that the new Foxdie is no longer mutating and that he still just has the older one that causes his accelerated aging, hence the name Old Snake that he has in MGS4. Raiden ends up going back with his girlfriend when he learns that he has a kid with her.