Santorini and Mykonos are not pickpocket friendly islands because they are too expensive for them to come. They couldn't afford the luxury of staying there. On the other hand, these are islands where you will be relieved of your money by restaurants, bars, taxis and hotels by paying double the rate charged on the other islands. But in this case it's your choice
The Athens metro is no riskier than any other metro in Europe. The line most used by tourists, which connects the airport to Syntagma Square, Monastiraki Square and the Piraeus, is the favorite of pickpockets who prefer to target those who seem to be holding on to their so-called anti-theft money belt (carry your money and valuables in an old supermarket plastic bag, you will never be targeted by any pickpockets)
Otherwise, in Santorini, Mykonos or Athens, just take the basic precautions as in all major tourist places. Watch your bags, your pockets, don't stick to other people going up or down the bus or the metro and everything will be fine.
Personally, I have been using public transport in Athens for more than 30 years without ever having had the slightest problem.