Storing Password in Databases in plain text vs Customer Needs

I think "bad practice" is an understatement. "Irresponsible" might be more accurate.

If it's worth to protect it with a password, it's worth doing it properly. Storing passwords in plain text is an embarrassing security breach waiting to happen.

If "security" is anywhere in your customers wishes (which I guess it is, since there are passwords), they've implicitly asked for a decent security system, which includes proper handling of passwords. They may not ask for "passwords being stored securely" (hashed and salted) because they're not the experts; that's what they hired you for.

Write a short, clear and jargon-free formal letter stating your concerns and concluding that in your professional opinion, it should be rectified. Address it to someone reasonably high up in the customer.

If they then choose to ignore your advice, that's their prerogative.

(Keep a copy of the letter yourself, too.)

If you can, a live demonstration works great. Ask the user to create an account with a password (not the password they normally use). Go into the database and retrieve, and explain that anyone who has access to your database (either by permission, or via a security breach) can simply go ahead and do this.