You should provide better way of communication to let tenant use mail, fax, overnight to send informationa dn give him /her your privacy policy and tell him how you will do to protect his/her private information.
As tenant reason of not using email is general and reasonable, just with this reason can not say he/she is bad tenant.
I usually will show tenants how to use encripted file in email. or use some securied cloud (like google drive) and tell tenants will remove those info on those cloud and keep information in very safe place.
When you ask such private information, it is federal law to ask you handle such information carefully and protect.