^^ Yes NEVER use fabric conditioner on towels , tea towels or nappies.
Fabric conditioner is an organic liquid similar to an oil, it makes fabric feel soft because there is a tiny amount of the 'oil' left on the clothes after washing, this is what makes them feel 'soft' and leaves the smell. The problem is the 'oil' also makes the towels/ nappies/ tea towels water proof so they are useless. If you read the 'small print' on a container of fabric conditioner it tells you not to use it on baby clothes as it increases the fire risk by making them more flammable.
Wash the towels ( without fabric conditioner) and then tumble dry. It is fine to dry them on the line and then tumble for just a few minutes. You can get tumble dryer ' softening balls' that you place in the dryer with the clothes and the balls ' rub up ' the fibres of the towels and make them feel soft and fluffy. You also need to only put enough stuff in the dryer at one time to allow it to 'tumble' freely or it will not dry soft and fluffy.