I am just wondering if it is okay to make Stripe account id (for Connect) and customer id visible on browser. Is there any way that a person other than its holder misuses by obtaining the ids? (for example, moving earned money to their account or change the person's information as a method of attacking)
All sensitive information coming from the account id requires your Stripe Secret Key (or that of the account, for Connect accounts). That being said, if access to those keys is compromised, having the account ids readily available just makes it that much easier for an attacker.
With public keys, I'm not sure you can even add a card directly to a user. Just create the card tokens and what not.