Julie here from Shopify Support.
The first thing you'll want to do is confirm that your store has customer accounts enabled. You can find out if customer accounts are properly enabled by heading to Settings > Checkout > Customer accounts and ensuring that either Accounts are optional or Accounts are required are checked.
If customer accounts are enabled, then it sounds like the affected customers do not yet have active accounts, which would be the reason why they are unable to login. In order for a customer to have an active account, they'll need to have received an email with a prompt to create a password.
You can find out if your affected customers have active accounts by heading to Customers > More filters > Customer account status > Active account. Once there, you'll just want to take a look at the listed customers. If you don't see the affected customers listed there, this would indicate they don't yet have an active account and you'll just need to invite those customers to create accounts. This will trigger an email which will prompt them to create a password. Once that's done, they should have no problems logging in.
If you do see that your affected customers have accounts, however, then there may be another issue at hand. If this is the case, please send me your store URL. I'd be happy to try creating an account and test out the login functionality here on my end.
As a side note, there's another post in the Shopify Community Forums on this exact issue. It might be worth checking that out to see if any of the suggested troubleshooting steps there work for you! You can access that forum post here.
Let me know how that goes!