I do wear Gloves during cleaning and sleeving the dried LPs.
I do not wear Gloves whilst assembling or putting the cleaning items away.
I have a batch of Sponges, and as I only Clean Six LPs in one session as the average, the sponges absorb hardly any water as a new one is used for an LP.
A Sponge might get used on a second occasion if I run out of Dry Sponges, when an additional LP is to be cleaned but this is rare now, the habit is for six
The Lens was dry when the T'cloth was used to clean the Protective Filter.
As said, I do not view this as a concern for the process of cleaning a LP, unless there is something to be added as a contribution that would identify it as a condition present that is of a concern.