I personally prefer to keep my own boobs contained, but mostly because I avoid tanning in general. (I'll sit on a lounger and read a book on the beach/by a pool sometimes, but I'd invariably be in the shade/under a parasol and smothered in SPF50 so I'd probably wear shorts and a bikini top for that. Also I've got massive knockers and my boobs can get a bit achy and uncomfortable without support).
However, I wouldn't be offended in the slightest if someone else had their baps out. If you're in a country where topless sunbathing is generally acceptable, then I think it's absolutely fine - I don't think it makes a difference whether you're at the beach or around the hotel pool.
There are definitely a few European countries where it's either prohibited entirely (Malta, Albania) or only allowed on designated topless/nude beaches. There are also some countries where it's legal still unusual and likely to be frowned upon. But in a lot of countries it's considered very normal and assuming that's the case where you are, by all means get the girls out if you want to. I've no time for people clutching their pearls over this - they're tits, and in a non-sexual context. It's fine!
The only place I've had an issue is in Mexico where the American guests were HORRIFIED that the Europeans had their boobs out
Well... yeah, but topless sunbathing is actually illegal in Mexico, though, at least on public beaches. I do think it's important to respect the law and customs of the country you're visiting. (I wouldn't give a shit about upsetting the American tourists though!)