Well, softness depends on the micron count. A micron is a measurement of length equal to a millionth of a meter or a thousanth of a millimeter, if I remember correctly a human hair is usually 100 microns, the lower the micron count the skinnier the wool fibers, the higher the micron count, the fatter the fibers. There are other factors involved that affect softness such as the bounciness (crimp structure) of the fiber and how tightly the yarn is spun, chemical treatments can also leave wool feeling harsh, but in general, the lower the micron count the softer the yarn, the higher the micron count, the harsher the yarn.
Wool fibers 30 microns and over are practically guaranteed to be itchy while wool fibers 20 microns and under tend to never bother people. Fibers between 21-29 microns may or may not itch depending on how sensitive your skin is. Most people who claim to have wool allergies don't and either have sensitive skin or have only been exposed to harsh yarns made from coarse wool.
Different sheep breeds produce different wools. Merino sheep produce wool that tends to have a micron count in the low 20's and is why it's known for its softness. Merino wool can go as thin as 12 microns, finer than cashmere but most commercial merino yarns are made with medium or strong wool merino which is around the low to mid 20's. All merino is not the same, a yarn made from 16 micron merino is going to feel alot softer than a yarn made from 23 micron merino. There are other sheep breeds that produce soft wool like: bond, finnsheep, cormo, polwarth, rambouillet, columbia but all of them have been bred and/or cross bred with merino.
Most wool yarn is made out of a blend of wools. I can't say what wool makes up yarn that's labeled "wool" but it would be from "dual purpose" sheep, meat sheep. Sheep that produce good meat tend to not produce good wool and vice versa so people try to breed happy mediums that can give decent meat and decent wool. Corriedale is a major dual purpose breed and produces wool 25-30 microns. Suffolk is a major meat breed in the united states with a micron count between 27-33 and I'm pretty sure that it's wool ends up in alot of domestically spun yarn.
Sheep aren't machines so some of them will produce finer wool, some coarser wool, and there's usually a difference of at least a few microns in an individual fleece. All this gets mixed together before being spun so even if a yarn contains mostly 26 micron wool but say five or six percent of the fibers are over 30 microns, it's probably going to be itchy.
There are also dual coated sheep: sheep that produce a down like wool and guard hairs: Shetland sheep Navajo Churro and Icelandic sheep are all dual coated. The undercoat is very soft but the guard hairs are usually very coarse which means that depending on how it's spun it can be soft or harsh. If the guard hairs are removed the yarn will be soft, if they're not removed, the yarn will be harsh. Cashmere is also a down fiber and everyone who talks about how wonderfully soft it is has yet to experience yarn made from insufficiently dehaired cashmere (shudder).
Now of course is when I talk about the downsides of fine wool. In general, the lower the micron count, the shorter the wool fiber which is why merino tends to pill alot easier than a wool blend yarn, the fibers in the merino yarn are shorter and wriggle out and form pills much easier. Coarse wool is long wool and it wears like iron so some things like outerwear and carpets require coarse wool. A tighter spun yarn would reduce the pilling but then the yarn would be heavy and dense. Another solution would be more, thinner plies: a six ply worsted weight merino yarn would be more durable than a four ply but this means more work for the spinning mills.
I have seen charts in books with different breeds and their average micron ranges but my google fu has failed trying to find a similar chart online. I can however direct you to two sites that list the different breeds of sheep:
Sheep 101 - Breeds of Sheep A-Z
Breeds of Livestock - Sheep Breeds
As for where to obtain soft yarn, alot of shepherds nowadays are sending off their wool to spinning mills and selling the yarn from their flock, instead of getting pennies per pound selling to a wool pool.
And about the acrylic/wool/mohair yarn: virgin wool just means that the wool came from a sheep's back and wasn't recycled. As far as I know all wool nowadays is virgin wool but apparently it used to be common practice some time ago for surplus wool fabric to be ripped apart and respun and rewoven into fabric called "shoddy". Virgin wool does not imply that it's soft, any wool that isn't reused is virgin wool. Adult mohair is also pretty itchy to most people at around 30 microns. The softness of acrylic, or lack thereof depends on how thin the individual acrylic fibers were made. Acrylic can be really rough and itchy, but if made fine, like in microfiber yarns, it can be amazingly soft.