I fail to see how you are being "discriminated" or "punished" by BT because they have "enhanced" the security of your email account. If anything you should be complaining that it has not activated on your family members accounts.
Did you "gift" your family the BTMail accounts by following the following procedure whereby they become responsible for the email account and have their own BTID in order to manage the account or did you just tell them to use the email account and it is still "owned" by you and managed by you which means only you can change the password and you can still have access to it?
See link about gifted email accounts.
Creating BT Email addresses | Email | BT Help
If you "gifted" the email account to them they will, if using webmail and not an email client, have to set up 2FA by following the procedure when they log in.
This will activate the 2FA and in their MyBT they will see that it has been activated by looking at the Your Details > Personal Details page
If you did not gift the email account to them the email account is still "owned" by you and managed by you and it should be activated on these accounts . If it is not you should contact BT 0330.1234.150.
As regards paying for an email client, there are many free email clients such as the Thunderbird email client which are as good as and probably better than Microsofts offerings that you could use and save your self money.
2FA does not work with email clients or email apps because the email client/app is device based in order to logon and use them and hopefully your device is secure to prevent unauthorised use where as webmail can be accessed from any web browser on any device any where in the world.
Hi
Thanks for the update on the Passcode issue. I am happy to report that has been removed for my account too, so life is simpler again. There was a brief spell when the Pass Code was changed for an "Are you a spam bot?" question that asked you to use the 'click on the photos with cars' system. That was an improvement as it did at least mean that I did not have to go and find my phone. The only trouble was that some of the little photos were of very poor quality so finding the presence of the chosen object was not easy.
Hope that you enjoy your time with BT Webmail, but do look out for the 'flags' problem. You will have noticed that when you read an email and then close it the system leaves it with a flag. Great idea if you want to see which emails you have looked at in this session, but it hides a 'trap'. Assuming that you have read 2 emails and closed them and next find something that looks like spam. So you flag that email and go to 'Mark as Spam and block sender' and then continue. What will have happened is that the senders of your two previous reads will now have been blocked and marked as spammers as well as the bad email. So if you are expecting emails from particular sources and they don't appear that is how they will have been blocked. You will need to go in to the list of blocked senders (Settings\Mail\Blocked Senders) and delete their addresses.
Regards
Pete