My friend does it and I argued with her that the dish sponge scrub should only be used for dishes and not the sink or the counter top because it will make the sponge too dirty for future uses for the dishes.
Yes, it's ok to wash other things with the sponge. You can easily use it for counter-tops, the sink, stove top, the floor - anything like that wthout a problem.
The sponge will become dirty, of course, as you clean with it, but the same is true of washing dirty dishes with it. If you can clean a sponge well enough to keep using it on dishes until it's soft and thin, you can clean it well enough to also use it on counters, sinks, and so on, the cleaning process is just the same. You will find the sponge is worn after fewer dishes, specifically - but the absolute amount of cleaning should be the same, just the extra wear and tear happened while cleaning other things.
While you can use the sponge to clean most things without issue, if you're using the sponge to wash dishes and food preparation surfaces you should be very careful if using it to clean messes that aren't people-safe, in case the sponge should become contaminated with enough non-food-safe substances to leave a residue. The aforementioned sink, counters, stove, and kitchen floor and in fact most household areas should all be fine, they are surfaces that you come in contact with regularly and should not leave anything on the sponge that regular cleaning won't take care of. But you might want a separate sponge if you're regularly using it for things like paints and solvents, mechanical lubricants, motor oil or adhesives, heavy chemicals, pesticides, or anything of that nature - that is, things you wouldn't allow in your living space without extra precautions.
Some religions will also not allow you to you your dishes sponge or cloth on anything other than dishes. I know some South Africans believe you can only wash dishes in your sink and you can only clean your hands and teeth in your basin. It is a sin to put a dish in the basin or clean your hands and teeth in the sink. They would therefor need a different cloth or sponge for each and every household chore.
This is rather dependent on what hygiene routine those other surfaces are subject to.
A big difference between dishes/used cookware/... and floors/furniture is that, especially as a cook, you are somewhat in control of what kind of "contamination" is on the former - former food and whatever microbes/yeasts like your cooking style.
Contrast that to a floor, especially one that is walked on in street or gardening shoes, or a countertop that is regularly used to, for example, unpack shopping bags that have been stood on a street - or that gets occasionally cleaned with harsh and residue-forming cleaners (and is routinely not used for direct food contact. There is a far wider spectrum of possible contaminants, including bacteria and virii that don't tend to live in food, parasites!, possibly metal shavings or tiny pieces of broken glass or stone, and whatever toxic organic or anorganic chemicals - could be gasoline/motor oil spills, freshly sprayed herbicide, drugs, battery juice, wood impregnation with creosote or mercury - you stepped in.
To keep separate, same color, sponges organized, marking them eg by cutting slits in or cutting/ripping off corners progressively helps: eg. fresh sponge that is used for things like non-dishwasher-proof knives and raw-garnish cutting boards, all corners there. Used for general purpose dishwashing, two corners same edge gone. For counter, two opposing corners gone (wouldn't suggest to use former-dishwashing for that!). Three corners gone, floor...
To me that's disgusting I feel like you're just adding the bacteria from your countertops on to the sponge and then spreading it all over your dishes. I wouldn't want to add to the bacteria that's already in my sink. I use 3 brushes. One for dishes. One for inside toilet bowl or on the seat and a brush for everything else.i use brush to do my dishes with sometimes I have a dish washcloth just in case i need it. I wil use the dish wash clith to clean or get a new one too. I will always clean the kitchen first with brush and wash cloth then I'll do the bathroom with them and when I do the bathroom I do the sink then the tub/shower then I will use only the wash cloth to wipe down the toilet sometimes the cleaning brush if its on outside but the seat i use wash cloth or toilet scrubber and inside just the toulet scrubber. The wash cloth that was used i put it in wash...if i used the dish cloth i could not reuse that on my dishes... Im very particular about things. If I can use a brush and not a washcloth or sponge then I will because it's a lot easier to clean a brush and to me it's a lot more sanitary.