Do dryer sheets effect the absorbation qualities of bath towels & dish

any type of fabric softner makes towel not absorbent.

yes. Try vinegar in the rinse cycle of your machine.

https://www.goodhousekeeping.com/home/cleaning/tips/a19506/fabric-softener-cleaning-product/

Yes. They put a very light coating of a waxy substance on your clothing, as does fabric softener in the washer.

I have started using cleaning vinegar instead of fabric softener in my washer's softener dispenser. It has been removing the mineral buildup from the washcloths I use in the shower that makes them stiff. I perceive no vinegar scent in any of my finished laundry. Costs less than Downy and I recommend that you give it a try. Regular distilled vinegar is less concentrated but will work the same if you cannot find cleaning vinegar that I purchase at my local Walmart.

Yes, the dryer sheets are not good for your clothes and I also understand the clog the dryer filters inside the machine.

A good use of those dryer sheets you already have if you live in the deep south or anywhere LOVE BUGS visit your area twice a year, they make a mess on the grill of your car and dryer sheets remove the residue they leave.

Dryer sheets coat the cloths to make them soft and static free, so it also coats the heating element in the dryer making it burn out faster. The coating keeps towels from absorbing liquid. I put a splash of vinegar in with the soap and fill the softener dispenser with vinegar (my towels come out soft and absorbent every time and we have very hard water in south central Texas).

Yes, indeed, I don't use them. They can clog your dryer filter too. Go for natural solutions like vinegar or detergent enhancers.

No drier sheets on towels. It coast them and they will absorb less.