People say Centralized Exchanges are not safe during wars. Go to web3 wallets and hard ones, even better!

Yes, they're right. Wherever you have got plugs and plug pullers, stay away from them during the crisis.

Having said that; what about your funds in banks and mutual funds?

They're way more unsafe than being on a centralized exchange. Why? Giant exchanges like the Super Giant Binance, OKX and Kucoin have made web3 dimensions available to you. You can bet on that. However, be warned about Coinbase as it is a highly controlled entity, stay away from them howsoever appealing they may appear.