We have banked online for years with no trouble. We have used conventional banks, credit unions and online only banks (Capital One). Agree completely with above opinions on 2 factor authentication and would add: if the institution offers 2FA via an app such as Google Authenticator or Authy I’d choose that over the text method. As also suggested use strong passwords and better yet a good password manager - LastPass, OnePass etc. Last point, Create/use very strong passwords and 2FA if available on your email account(s) as they are often the gateway to all your online presence. Embrace the flexibility and convenience, but do so wisely.