A towel absorbs in two places, and each one can be blocked separately
Cotton is absorbent for two reasons, and they fail independently. The first is the surface chemistry: cellulose is covered in hydroxyl groups, which water likes. The second is geometry: between the fibres there are gaps narrow enough to pull water in by capillary action, and that is where a towel actually holds its water — not inside the fibre but between them.
Now the two faults. If those gaps get filled, the towel goes stiff and boardy: it still absorbs a little, slowly, because the surface chemistry is intact, but the capillary space is gone. That fill is usually calcium soap — detergent that met the calcium in hard water and turned into an insoluble salt that deposits between the fibres. If instead the fibres get coated, the towel goes slippery and stops absorbing altogether, because you have covered the hydroxyl groups with something that repels water.
And that coating is fabric conditioner. This is the part worth sitting with: conditioner is a cationic surfactant plus silicone, and its entire mechanism is forming a film on the fibre so that fibres slide over each other and feel smooth. A film that makes fibres slide is a film that water cannot get through. So the bottle you bought to make the towel soft is the bottle that makes it non-absorbent and, because that film is fatty, feeds whatever grows in a damp bathroom. Soft and non-absorbent are the same fact seen from two sides.
Three faults, three answers
Stiff and chalky, that still absorbs slowly, is calcium soap between the fibres. Fifty grams of citric acid in a basin of warm water, thirty minutes, then a normal wash with a modest amount of detergent and one extra rinse. The acid dissolves the calcium salt; the extra rinse carries it away. Rinsing is the part people skip, and it is the part that matters, because detergent left in the fibre crystallises as it dries and that crystal is hard.
Slippery and non-absorbent, where water stands on the surface, is a film. It needs heat and detergent: 60 °C or above, because that is the range where a fatty film melts, and cold water simply cannot shift it. Run that load with no conditioner at all, add a rinse, then test with a drop of water. From then on: no conditioner on towels, ever, or at most once a month.
Sour or musty, with dark specks near the hems, means something is growing in the film. Oxygen bleach — sodium percarbonate — at about 20 g per litre, 60 °C, an hour, then a normal wash and a full dry in sun if you have it. Not chlorine bleach: hypochlorite oxidises cellulose, so the towel loses strength and yellows, and it reacts with conditioner residue to make chloramine smells that are worse than what you started with.