I confess to being a bit perplexed by the usage in the industry of fabric softener and fabric conditioner.
As far as I can tell, the manufacturers use these terms interchangeably, and products advertised as "fabric conditioner" can be labeled "fabric softener" and vice versa.
Often those labeled "fabric conditioner" may be loaded up with more exotic fragrances, and if you don't want your laundry smelling like a cheap whorehouse, you might opt for a "free and clear" product which I invariably find is labeled (and advertised) as a softener.
So the nub of this problem is which will leave one's towels both soft and absorbant?
Well, depends. My take on this is that they all have long chain fatty acids in them, so they all have the capability of rendering fabrics less water absorbent. Makes little difference if the fatty acids come from cows, chickens, soybeans, or avocados.
Previous suggestions to tumble rather than line dry, or a combination thereof, will leave a softer towel the absorbency of which is not compromised. Vinegar doesn't seem, in my experience, to influence softness or the lack thereof much, but it does seem to cut down on residual sudsing in the final rinse.
Hard water can result in harsh results and STPP is probably the best water softener one can add to one's wash water. I have however seen statements here that STPP can impart harshness by adhering to fabric fibers. I would think this runs counter to the way STPP works, by complexing with hard water minerals so that they no longer form sticky precipitates with detergents and don't stick to fabrics and do get rinsed away in the final rinse(s). Of course if one uses too much of anything it can not get rinsed away and cause problems related to that situation. And perhaps STPP is reactive enough that if it doesn't find hard water minerals to latch onto, it might try to latch onto fabric fibers. Just speculation there, but if that is the case, one should be careful not to add more STTP than is necessary to soften the water and break mineral laden dirt from the fabric. In any case, I've found it helpful to monitor the sudsing during the rinse cycle. If the suds don't go away it can indicate too much detergent for the level of water hardness and fabric soiling, which in turn can result in harsher results. For a while I had to resort to adding little or no detergent (powder or liquid) to loads of towels to keep residual sudsing down. The final results were softer than before, and the towels (for bath) were basically clean from the hot wash water and multiple cold rinses used. I was able then to gradually add much more limited amounts of detergent to maintain those desirable results.
In other words, more is not necessarily better.