Avoid anything cement-based (concrete, FireSlate, etc) or many of the softer or porous natural stones due to the potential of the vinegar to etch those materials, or the dyes and paints to stain them. Even granite.

Soapstone is non-absorbant, and non-porous. It can, however, be superficially stained or discolored if a damaging liquid is left standing on the surface for long periods. If that happens, just give it a light scuff sanding to remove any surface imperfections.

Soapstone is relatively soft though, so it can scratch.

With all the things you'll be throwing at this countertop, I hate to say it, but an inert man-made synthetic might be your best choice for performance, but it might not fit the aesthetic.

You could do concrete and give it an epoxy film finish. An epoxy film is near bulletproof when it comes to stain resistance, but heat (hot pot from a cooktop or oven) can damage or lift the film.

mongoct- you understand the issue well! My current wet area has mica counters, a ceramic laundry sink, and ceramic tile floors. Clean up is simple, but it is a "no guest zone" so I don't have to worry about the aesthetic.

Is the epoxy film something that is just painted over the concrete? If so, I could buy some and try out the concrete concept on a sample.

Years ago I used to do a lot of concrete countertops. I'd use the epoxy on commercial slabs; bar and restaurant countertops, etc.

I'd use a 100% solids two-part epoxy. It can be put on to thickness, it cures clear, it's non-yellowing if exposed to UV, and is pretty much bulletproof concerning anything liquid that might be thrown at or on it. Except heat, like a hot pot.

With the proliferation of DIY concrete countertops these days, there are probably DIY kits out there for purchase.

You also might consider a stainless laundry sink and porcelain tile counter.

In our laundry room/my morning vanity room, we did a stainless laundry sink that was from Lowe's and under $100. I happen to have formica in that room, but my kitchen does have porcelain floor tile on the counter, which is very durable.

If you would find it not to against the bathroom look, you could also use a stainless one-bowl sink with sideboard drain.

http://www.plumbersurplus.com/images/prod/5/Oliveri-222-0-rw-8369-3924.jpg

I have one on my kitchen island, and find it very functional.