There seems to be a few " Red Limes".
Some of the Rangpur types are called Red Limes, but they seem to be pretty much Rangpur with orange or darker orange skin.
https://citrusvariety.ucr.edu/citrus-varieties/category-or-type/rangpur-limesNone of there are particularly red.
A lot of these are very similar, possibly some have been lost and mixed up over the years ?
Excalibur Red Lime is on this list, not strictly a Rangpur, but not red pulped either.
There are also Red Limes that have red skin and red pulp, a little more mandarin like with sour juice.
Anybody growing any of these ?
Some on the Citrusgrowersforum posted pics years ago.