I have three cats which all have medium to long hair. They shed almost continuously, even after being brushed. "Their" room is the laundry, that's where they're fed and, if they choose to, sleep. The laundry is accessed either from the kitchen or the toilet, and the toilet has another door to the bathroom (it's a weirdly designed house!)
I don't let the cats into the kitchen because they might jump on the table or the bench when I'm not looking. (They would never do it when I am looking because they know I'll tell them off!) It's easier to have a rule that they're never allowed in there than sometimes (e.g. because I'm in there too and can supervise them). I don't believe cats are mentally capable of making that distinction.
So, this means that for them to be able to access the rest of the house they always have to go through the bathroom. The problem is, just walking through is enough for loose fur to come off them, which then floats around the bathroom, some of which eventually settles on the towels. I don't know how many people have wiped their face with a towel that had just a few cat hairs on it but I can tell you it's not pleasant! The fur immediately sticks to my wet skin. My cats' fur is very fine so I get a tickling sensation until I eventually manage to pluck the hairs off. (I'm not allergic to cats, it's a purely physical reaction).
Recently, I had the idea of keeping my bath-towel in my bedroom (where they're also not allowed to go for much the same reason, I don't like waking up with hard to remove cat hairs on my face and in my mouth). I then take the towel into the bathroom with me just before I wash and remove it again when I leave the room. However, after trying this I realised that I no longer have a towel to dry my hands on after washing them. I don't usually have a hand-towel hanging up in the bathroom but if I did it would have the same problem: after drying my hands they'd be covered in cat fur.
I don't have enough room for a free-standing cabinet and I'm renting so I can't make any modifications to the house. The kitchen, laundry, toilet, bathroom and hallway are the only non-carpeted areas of the house so moving their food bowls, water and toilet into another room isn't practical. Short of moving to a better designed house, what can I do to keep the cat hair off my towels so that it doesn't end up on me when I'm trying to dry myself?