I suppose some beaches may be a bit uptight about it, but most beaches over there have been allowing topless and skimpy bottoms for decades. I think you would find it very hard to find a beach in Spain that would find that inappropriate. Possibly more would find it inappropriate in Greece. Now in France I doubt anyone would bat an eye over that.
While it is allowed almost everywhere, I would not recommend it, you would definitely get judged a lot. But it might also depend on the beach in question. Just dress like they dress if you are worried about being judged/standing out, if that makes sense. There are also nudist beaches you can go to, they are not at all sleazy - more for older people (40+), families, and a somewhat more alternative crowd. In general, at least where I live (Scandinavia), thongs are considered not classy and a bit of a Eurotrash look.
Shouldn't be a problem - I haven't been on an European beach for a while but large numbers were topless in thong bikini bottoms the last time I was there. As you say, you do it mainly for tanning and have shorts or a wrap for walking around.
On Crete they have seen worse, on Ibiza too. (Both are booze, drugs & sex places). Italy, maybe. Other Spanish coasts, maybe. In Croatia they have some nude beaches. Morocco and Tunisia, Algeria are certainly places where you should cover up more.