Triple H will always have his share of haters for any number of reasons. I'd say the most prominent reason is the refusal by some to accept that his success wasn't handed to him. Left & right, you'll have some pop out of the woodwork and bitch about how Trips is only where he is because he's been banging Stephanie McMahon since she was of legal drinking age. They ignore the fact that the man's pretty damn talented and very good at what he does. They conveniently ignore that he was a founding member of DX, they seem to forget the great feuds & matches he had, and leave out all the memorable moments he was part of during the Attitude Era. Triple H was someone who had the goods to be a major level player in WWE long before he got involved with Stephanie McMahon. If you want an example of being placed in a high profile spot due to familial connections rather than having the ability to justify having it, look at Brooke Hogan's time in TNA.
Triple H in this role has been definitively helping the careers of a number of young guys on the roster; especially Daniel Bryan, all three Shield members and Cody Rhodes. People have been wanting to see Bryan get a major main event singles push and he's getting it. They want to see The Shield kept in a high profile spot with the US & tag titles, they've got it. They want to see Cody Rhodes break on through to that next level in his career, it's looking like he's on his way. Triple H, and Stephanie for that matter, have also helped inject some fresh life & interest into veterans like Goldust and Big Show. Goldust was, pretty much, a nonfactor in WWE, and pretty much all of wrestling for that matter, during the entirety of the 2000s. During his match with Randy Orton on Raw a few weeks back, which was a great showing btw, when was the last time Dustin Rhodes received a pop like that or such interest from fans? When fans rally behind babyfaces in the hopes of seeing the heels ultimately get what's coming to them, because the heels are such pricks, it means the heels are doing their jobs of generating disdain for their characters among the audience. In an age where smarks populate the wrestling landscape and are more interested in putting on their own show rather than suspend disbelief, what Triple H & Stephanie have been able to do as heels the past 6 weeks or so has been great.
I think another problem that some have, not all but some, is one that's become pretty common among internet fans: The "they're not doing everything I want 'em to do or the way I want it done" and/or "things aren't moving fast enough" complaints. In some aspects of the angle, metaphorically speaking, WWE probably zigged while some fans felt vehemently that they should have zagged. Because of that, they piss & moan about it with some using Triple H's presence in the storyline as a scapegoat or complain that the storyline isn't progressing quickly enough. If it went any faster, then you'd have some of the same fans and dirtsheet writers complaining that WWE is rushing through things and not giving it enough time to get fleshed out.
I don't think the angle is perfect or anything, I do believe that Trips is sometimes involved too much. We don't have to see him in half a dozen segments, but that's not nearly enough for me to spew hate all over the angle because his presence isn't hindering it in my opinion.