I don't usually get on this topic but I would like to point out that this is a phrase that has been around for awhile, particularly among Pentecostals who at one time took this "not a religion" statement very, very seriously.
Most still say it, like Bill here, even though the meaning has changed and many today aren't even aware it meant a lot more than it once did. The evangelicals I've run into are shocked and sometimes don't believe the extent that was once taken when I tell them.
That's been my experience.
So 100, even 50 years ago, when they said they Weren't a Religion they really meant it. No permanent buildings, no membership rolls to a legal, government registered church, even no robed choirs, and sometimes no musical instruments - particularly organs.
The Azuza Street warehouse in Los Angeles where Pentecostalism first flourished was deliberately torn down and the lot divied up for the express purpose of preventing any sort of pilgrimage to it (the area get's a healthy amount of tourism from it today regardless).
Permanent buildings, robed choirs, etc. exist today in most major Pentecostal and Charismatic churches. There are still storefront churches but they are largely seen as just starting out. Pentecostal churches started registering as legal entity in WWI so they could claim as consciousness objectors, but you would be hard pressed to find any of those early churches that still believe that today.
What it implies is emphasis on the worship services, something that was taken to the extreme with the Latter Rain Movement of the 1960's which is where I think the old definition lead to its end. IMO it was also a statement against the "denominal churches" which many of those folks came out of. The Sunday worship service I believe is a result of this as well as folks would go to their denominal services in the morning and the storefornt church or Tent Revival at night.
That the old definition didn't last in face of the more stable, permanent churches shouldn't be a surprise. It is also largely contended (at least in my Bible Colleges) that the only reason they were against electric organs and robed choirs is because those early churches were small and couldn't afford them
.