Is Binance.com ID Verification safe?

Regardless of which crypto exchange you use, you'll likely have to end up giving up some form of personal information for them to verify your identity. This is purely for KYC purposes as crypto (actually in banks too) is often used for money laundering/terrorist financing.

Fortunately, Binance is the largest exchange in the world at the moment (if I'm not mistaken) in terms of active users and transaction value. Moreover, they've also applied for a crypto license under MAS updated Payments Act which covers crypto now, so I wouldn't be too concerned.