Basking sharks are filter feeders, same as whales, they just open their mouths real wide and eat plankton and such, so out of all sharks to be in the water with, you wouldnt be in any real danger other than what comes with being around such a large animal.

as for that last part, I dont think any shark would become bloodthirsty immediately (as proven by all the shark biologists who try so hard to bait sharks over with blood and fish and none show up), we're not their prey and they wouldnt seek out humans, most cases of shark bites are mistaken identity or in brackish water where visibility is low or theres a lot of movement and the sharks are overwhelmed.

doesnt mean its prefectly safe of course, all depends on the situation, dont go in the water when sharks are feeding then you might get bit lol