INTERNET LODGE 9659 (UGLE)
The United Grand Lodge of England (UGLE) constituted Internet Lodge No. 9659 in 1998. It is a regular, recognized lodge that is open to any existing member of the UGLE, or any other Grand Lodge that is in amity with the UGLE (see the list here). They hold a physical meeting in an approved English Masonic lodge three times a year, moving around the UGLE's territory with each meeting. The password-protected members only part of the site deals with the minutes and day to day business of the lodge (they do NOT actually meet over the Internet). They have members from all around the world who are real, authentic, regular, recognized Freemasons, and each meeting is followed by a traditional Festive Board for attendees. The catch is that its members must first be initiated, passed and raised in their own lodge before they can petition to join Internet Lodge. And each member must agree to pay all regular UGLE annual fees, along with their lodge membership.
What I do not know is if you can demit from your Mother lodge, become an unaffiliated Mason, and then still be allowed to join Internet Lodge. I know you must technically be a Mason in your home jurisdiction when you join, but I don't know if you actually are required to maintain a lodge membership in your home jurisdiction. I suggest you contact both Internet Lodge's Assistant Secretary, as well as your own Grand Secretary to make sure the proper rules are followed.
(Since I first posted this, I have received messages from some US brethren who say they no longer belong to any US lodge or grand lodge, and ONLY have membership in Internet Lodge, making them solely a UGLE Mason.)
IRELAND LODGE 2000 (GL of Ireland)
Similar to Internet Lodge is Ireland Lodge No. 2000, a regular, recognized lodge chartered in 2000 by the Grand Lodge of Ireland AF&AM. Like Internet Lodge, members must be Master Masons in good standing of a jurisdiction in amity with the GL of Ireland, and its rolls are comprised of an international group. They meet four times a year, at different locations throughout Ireland. The June meeting is always held in Dublin, and is traditionally the one with the most foreign visitors. They also have a secure, online chat room and hold monthly gatherings (except in December) via the web. Degrees are not conferred by the lodge, and Masons wishing to affiliate with them must be initiated, passed, and raised in another lodge first.
CASTLE ISLAND VIRTUAL LODGE 190 (GL of Manitoba)
Finally, the Grand Lodge of Manitoba (Canada) chartered Castle Island Virtual Lodge No. 190 in 2012, and to my knowledge, it is the only truly Internet-based lodge in the world working under a charter from a regular, recognized grand lodge. (It's also the only lodge on Earth where you can be home 10 seconds after the last gavel falls!) The lodge meets online on the 5th Wednesday of those months that HAVE 5 Wednesdays, at 7:00PM Central Time. Visitors are welcome, but must first contact the Lodge Education Officer at Leo.firstname.lastname@example.org or the Secretary at email@example.com to be given access. They must be from a jurisdiction that is in amity with the GL of Manitoba, and send a photograph of their current dues card along with a brief biography to the LEO to be "admitted" to meetings and the secure portion of the website.
For the meeting itself, visitors must have a computer equipped with a microphone and camera, and they use Webex technology as a secure online conferencing method (originally, the lodge was designed as part of the "Second Life" virtual 3-D community, but a more secure meeting system was desired). Ritual used is the Canadian Work (a variation of Britain's Emulation ritual), and visitors are expected to tyle their own computer's location during online meetings.
If you are resolved to give up membership in your home lodge and grand lodge, you may first join Castle Island as a dual member, pay dues to the lodge and the Grand Lodge of Manitoba, and then demit from your home jurisdiction. You will have to be investigated and voted on, as with any other regular affiliation. For details on doing that, contact the Secretary. (It can and has been done before, but not often - their current Tyler just did this from his original lodge in Italy.)
AMERICAN JURISDICTIONS PERMITTING OUT OF STATE MEMBERSHIP
I have received a message that claimed the GL of the District of Columbia allows Masons to join their lodges without actually being a resident of the District or the immediate surrounding regions in Maryland and Virginia. But because DC has suspended fraternal relations with both TN and GA, this complicates the issue. Under the current circumstances, I don't know if DC is willing to act as a safe haven for disaffected Masons from those two states. Please contact them directly to clarify this.
Also, the Grand Lodge of North Carolina and the Grand Lodge of Alabama have no residency requirements, and allow multiple dual-memberships. There are undoubtedly others of which I am unaware, and with recent events, more jurisdictions neighboring troubled states may very well be making changes to these developments as I type this. It is probably best to simply contact the Grand Secretary in your neighboring state and simply ask if you might be permitted to affiliate or join outright if your permanent residence is outside of their territorial borders.
TAKE NOTE: In certain cases, discretion may be vital when doing this. You may wish not to disclose your identity when making your initial contact out of state in case your own home grand lodge is vigorously attempting to prevent their own members from defecting. Do your research and find out all procedures required to transfer out by both grand lodges before you reveal yourself. There are generally territorial rules that have been enacted specifically to prevent what you are attempting, which is why the above alternatives are most dependable.
Also, be aware of the timing involved when it comes demitting in your state. Different grand lodges demand very different paperwork, such as letters of good standing. If at all possible, retain your current paid-up membership in your home jurisdiction, at least until you have a dues card or other official notice that you are a full member in your new out of state lodge. Only then can you safely pull the plug on your old one. And always be aware that an 'honorary' membership is not the same as a full fledged, dues paying, card-carrying membership in another lodge. Honorary memberships carry zero weight when it comes to Masonic jurisprudence.
A message specifically from a Tennessee Mason this afternoon about that particular grand lodge's process:
You must write to the Secretary of the GL of Tennessee and ask for a Certificate of Good Standing. This is NOT the same as a demit. Do not demit. This certification allows you to remain a member in good standing while you seek membership elsewhere, in another jurisdiction. You will need to get a new Certificate every year until you find a new home. If you are a just and upright man and Mason and want to join a regular lodge of Masons, you are not required to remain a member of the Grand Lodge of Tennessee in order to enjoy the fellowship and fraternity of the oldest organization in the world. Please be calm and do not demit your membership until you find an alternative.