I use Safari on iOS and I'm having issues connecting to a new bank.

Various components can influence the authentication process, one of them being the browser's settings.

Here's what you can check on your iOS/Safari's settings to ensure the process works fine.

1. Make sure you're not using Safari's Private Mode.
   
2. Check your Safari settings. Go to Settings → Safari and look for "Prevent Cross-Site Tracking" and "Block All Cookies". Disable them and try again.
   
3. Disable any Content Blockers that may be active on your Safari and try again. Go to Settings → Safari → Content Blockers:
   
4. Make sure you're not using incognito/private mode on your browser as this might also affect the process. 
5. Clear your cookies and cache.
6. Try changing your default browser to Chrome temporarily under Settings → Chrome: