Should you connect your washing machine to a softened water supply? Before answering this question I need to point out that there are two different ways to soften the water supplied to a washing machine.
One is through electronic devices attached to the outside of plumbing pipes (the effectiveness of which is often disputed)..
The other is a full softening system using chemicals, which as far as I know is less common in the UK than in other countries such as the US).
Some washing machine manufacturers advise against connecting their washing machine to an full artificially softened water supply (not the electronic water "conditioners" mentioned above) as it can make the water too soft for washing. If you don't reduce the amount of detergent it can result in over-foaming, but less detergent can give poorer wash results.
So modern washing machine detergents can be less effective in very soft water because the detergent does not dissolve as well. This can cause detergent deposits on laundry.
Using a washing machine with an artificially softened water supply should not damage the washing machine, but wash results can be affected due to the detergent not dissolving properly and leaving detergent residue on laundry.
This may be counteracted a little by using an extra rinse option on the washing machine if available. This advice may also help If you live in a (naturally) very soft water area.
My current understanding is that this advice is relevant to chemically softened water rather than electronically conditioned devices mentioned above.
These claim to condition the water and prevent limescale build up rather than physically soften water.