In my opinion it was at the 2015 Royal Rumble when everything started to switch as far as the fans go and their hatred of Roman. Then the booking for the remainder of the year didn't help matters because he was still protected. I will say that at the end of 2015 things started to look up for Roman as the WWE was actually booking him quite well and when he finally won the World Title from Sheamus the fans actually liked it. Sadly the good booking of Roman didn't last and the problems came back again.
The biggest comparison people do is when they compare Roman's current booking to how the WWE used to book John Cena. Unfortunately for Roman he is going through the same tough time that John had gone through because the WWE never bothered to humanize Roman to allow the fans feel sympathy for him and seeing him have to fight against the odds. Seeing him come up short in a feud or losing clean a few times would help not just give some fresh ideas for him, but would allow Roman to have to work his way back up.
It's really simple the reason why the fans don't like Roman is because of how rarely he loses or looks human. From his robotic promos to how rare it his he actually suffers a clean loss really doesn't help his case to be looked at as someone that the fans can invest in and like. I don't think that the WWE need to turn Roman heel and even though I do think he would be more comfortable as a heel I don't think it's necessary as they could accomplish the same thing, but letting loose a big match or two clean instead of always being protected. Looking at his booking all the WWE need to change is instead of booking Roman like a "Super Human" they need to let him be booked like a human where he comes up short or doesn't get his way like a normal person.