Not all banks require SMS. I use Chase bank and the two factors are my debit card and my PIN. I don't use any app, but instead just go to the ATM or talk to a human. Some things, like wiring money, have an extra charge if you don't use the app.
A major downside of this is that if someone did figure out how to withdraw a bunch of my money from my account, I wouldn't notice until I go to the bank, which I only do once per month or so. I wish my bank had an option to send me an email on every transaction, but as is I have to go to the ATM and request an email with the recent transaction info.
Partially as a result of this limitation, and partially because I enjoy playing the "Where's George?" game (which involves using cash), I pay for everything with cash and only use my debit card for withdrawing cash. I've heard that it's possible to get an ATM-only card for this purpose, so I will probably do that eventually, so that if someone gets my card information they will not be able to make online transactions.
A major downside of this is that if someone did figure out how to withdraw a bunch of my money from my account, I wouldn't notice until I go to the bank, which I only do once per month or so. I wish my bank had an option to send me an email on every transaction, but as is I have to go to the ATM and request an email with the recent transaction info.
Partially as a result of this limitation, and partially because I enjoy playing the "Where's George?" game (which involves using cash), I pay for everything with cash and only use my debit card for withdrawing cash. I've heard that it's possible to get an ATM-only card for this purpose, so I will probably do that eventually, so that if someone gets my card information they will not be able to make online transactions.