Anyhoo, why would one wear gloves when handling statues, Lostris?
I can't claim to be an expert on this, but having been around a museum as a volunteer I've gained some information. I've read some about it, too.
It may not always be necessary to wear gloves when handling stone artifacts such as statues, but most professional conservators will. For one thing, all stone artifacts acquire a natural patina over the years, and this patina can help protect the most delicate carvings on a piece. The oils in our skin and simple handling with our bare hands can wear down this patina and render the piece more vulnerable.
More importantly, many of these ancient Egyptian statues were brightly painted, and often there are still extant remnants of the paint. (The face of the Great Sphinx still has a bit of paint on it, in fact.) The oils in our skin are quite corrosive and can damage or destroy the remains of paint.
The case for wearing a face mask is similar. The carbon dioxide we all exhale when breathing is very damaging to ancient paints, as is the humidity in our breath. This is one reason the Egyptians have had to close off the spectacular tomb of Nefertari in the Valley of the Queens--many years of trapsing tourists significantly damaged that tomb.
In our own exhibit at the Field Museum we have the offering chapel of a 5th Dynasty prince named Unis-ankh. Within the chapel is his false door, which is about ten feet tall, two feet thick, and weighs some seven tons. There is glass plating covering the bottom six feet or so of the false door so that no one can touch it and damage the pinkish hue the Egyptians applied to make it resemble pink granite (it's actually limestone). However, the top four feet or so of the false door is not covered by glass. Most people may not be tall enough to reach over the glass and touch the door, but over the years the breath of the hundreds of thousands (millions?) of people who have stood in front of the door to admire it, has caused obvious damage. The pinkish hue above the glass sheeting has considerably faded; it's plain to see when compared to the majority of the door behind the glass. This drives our consulting Egyptologists nuts but no one has done anything about it yet.