Librem Mail uses a Sender Framework Policy (SPF) which basically says: “Do not allow mail from firstname.lastname@example.org if it does not originate from a Librem One mailserver”. So if you try to forward your @librem.one mail via alternative mail providers it will probably fail. The same will happen if you try to forward your personal mail to your librem.one mail using a mail service that uses SPF. The librem.one mailserver will see that your personal mail is forwarded by an unauthorized mail server and block the connection.
Here’s a more extensive explanation of the problem (with possible solutions) for the tech savvy: https://tools.ietf.org/html/rfc4408#section-9.3.