I'm open to correction, but any observation of a red-eared slider feeding on bird eggs would be previously unknown to science, so obviously not a common occurrence by any means. A wild red-eared slider foraging on land would also be a first.What was the point of bringing up a post that is really old hat. Our Government authority has long declared this species as invasive - end of. Nothing new from your ramblings I'm afraid, whilst I personally have watched a large individual consuming the contents of a great crested grebe egg many moons ago.
No different to your Fisheries and Game department labelling European Starling and House Sparrow as invasive unwanted pests.
If the egg was in the water, then the turtle may not have been solely responsible for its fate. Perhaps even a careless grebe parent could have been to blame.
A red-eared slider would have to get each individual egg into the water in order to predate a grebe nest. Nothing like a fox or mustelid which could likely (easily) devastate multiple nests in a matter of minutes.
Red-eared sliders are invasive in New England, too, and I'm not saying that invasive species should be ignored. But nobody accuses red-eared sliders of devastating native ducks, and people are more concerned about them outcompeting native turtles.
This isn't a concern in the UK, but I listed some likely potential threats that they pose.