Re Tom Hanks, apparently when they were casting for Bonfire of the Vanities, he objected to Melanie Griffith on the grounds she'd just had a baby (Dakota Johnson!) and wouldn't be "in shape" enough.
I think Hanks is generally a decent person. But he's a leading man. For one thing, that always means he carries a huge amount of pressure on his shoulders to make each project work, and he also has massive personal pressure to keep up his star status, and there are very few individuals who can cope with that over many years without occasionally cracking (when an actor isn't expected to get an Oscar nomination for every role, they can be much more easy-going than those few who
are expected to do just that).
It's also just a fact that sometimes styles and skills do just clash. Take Richard Briers - a lovely man, but a great worrier, and when he was doing Ever Decreasing Circles he got so anxious about his own performance that he ended up asking for a different director to push him harder. He was deeply embarrassed about seeing a good director sacked, but it wasn't just some exercise in star power. Sometimes the chemistry isn't working.
The fact that Hanks and Winkler clashed is really surprising, but I really doubt there was anything beyond professional neuroticism behind it.