While mercury thermometers are now "extinct," glass thermometers still survive. They mostly use an alcohol-based fluid instead of mercury.
Also, digital thermometers can be used either orally or rectally. Just remember to put the probe cover on. (Sometimes there are "red' and "blue' probe covers, but usually just the one.) There are also red and blue probes.
As I have lamented before, I haven't had a rectal temp taken, (except for when I take my own) for years. In the Navy, we only used them in kids, patients who have had oral surgery, etc, and cases of heat or cold injury, where an accurate core temp is essential.(Occasionally, if we got an abnormal oral temp, and found the patient had just had something hot or cold to drink, we'd do the RT for accuracy sake) As for the VA, there's just no way.
Pity, I actually prefer them. I have a small mouth, slightly triangular upper jaw, sensitive teeth, and a deviated septum which forces me to be a mouth-breather most of the time. Even so, the VA just doesn't do RT's without a direct doctor's order.