how recent this trend is

I think the real answer actually predates the year 2000, so you may not find a satisfying answer. The truly negative portrayal of homosexuality started going out of fashion in the late-80's. During the 90's, they were still stereotyped and being gay was still sort of "icky", but I can't think of any genuinely negative portrayals past the 2000's. Unless you count a few villains who were evil in addition to being homosexual, rather than because of being homosexual.

You might be interested in The Celluloid Closet. It's a documentary about how the portrayal of homosexuality in film evolved over the last century. Unfortunately, the documentary came out in 1995, so it won't uncover any post-2000 films... but even in the documentary, all of the more recent (90's) films portray homosexuality in a positive or neutral light.