I think the usual problem with CGI is the way the scenes are directed, rather than the effect itself. There's a tendency to show CG entities making ridiculous moves in-frame, such as moving from a distance to inches from the camera at great speed - no real entity would ever be filmed in such a way and it creates an instant disconnect.
When you look at Jurassic Park's CG, which is still considered a benchmark despite being an early example, the creatures are almost always seen at a reasonable distance. On the rare occasions they're filmed up close, they're moving at a naturalistic rate in relation to the camera. You still have the sense that they're filming something real, because it's done in the way that you would film something real.
