Eight ball billiards: even if the cloth is brand new, they use Carnauba wax. They like the tables to play long and slippery. Southgate uses water and a little alcohol which actually keeps it shorter with more friction.
Does polish affect the fabric? Well, yes, a little. Some of it gets onto the cloth. Long term, I don't think it hurts it.
Here's my preference: use Aramith ball cleaner only. If you are using an electric ball cleaner, then wipe off as much of the Aramith ball cleaner from the balls with a clean dry rag before running the balls through the machine, to prevent buildup.
Clean the table: vacuum after every game. Don't be aggressive with the vacuum. Go soft and slow to protect the cloth and make it last longer. The better quality the vacuum, the better job it does. Don't use a rotating brush on the cloth. Make sure it has a wide brush attachment and not a flat, plastic one which scratches up the cloth.
If the cloth is not brand new, then also wipe the table bed with a slightly damp and clean microfiber cloth (Walmart), going WITH the grain of the cloth (if you are standing at middle of the table along the long rail, then your motions will go from left to right).
This will make your table play slightly longer and slightly more slippery.
We do this now at the tournaments instead of vacuuming if it is very inconvenient to vacuum. It is also easier and quicker. The tables play great.
Taking the wax off at eight ball billiards: if the table will play too short for your taste without the wax, then try to play with the wax on. If it is too slippery for you, then you can use your hands to wipe some off (difficult) or you can use a dry rag or even a slightly damp rag. Beware that by using a damp rag you will not only be taking the wax off, but you will be putting water (moisture, friction) on the balls which will cause it to play even shorter. Experiment to see what you prefer.
If you are a tournament player, you should learn how to play in all conditions:
1) brand new cloth and no wax
2) brand new cloth with wax
3) moderately new cloth with and without wax
4) old cloth with and without wax
5) old cloth with water as a cleaner
6) old cloth on an old unheated Brunswick
I am sure there are even more possibilities. It boggles the mind.