This problem was caused by the expiry of an intermediate signing certificate a few days ago, but Mozilla is yet to admit this is the case.
In an update to an old blog post, issued at 4.25pm EDT on Monday, (6.25am AEDT on Tuesday), Mozilla said version 66.0.4 on Desktop and Android and version 60.6.2 for the extended support release would fix the extensions issue.
"This release repairs the certificate chain to re-enable Web extensions, themes, search engines, and language packs that had been disabled (Bug 1549061)," the foundation said.
This writer uses the Firefox version issued by the Debian GNU/Linux project and on Tuesday morning a fix was issued.
While it initially appeared that Mozilla was using the incident to try and get users to submit telemetry data, that does not seem to have happened.
As can be seen from the writer's own browser, the settings for collecting telemetry data are still greyed out as they were prior to this snafu.
Update: In response to a query on Tuesday AEDT, a Mozilla spokesperson told iTWire on Wednesday: "We have teams working across multiple time zones to resolve all remaining issues. The cause was an intermediary certificate expiring without being signed, and we're very sorry for the inconvenience this has caused. We are not using the incident in order to gather data. Rather we found that the Studies program was our best vehicle for delivering an interim fix.
"Studies are enabled by default for all users of Firefox. While they were used for an initial fix to address the certificate issue safely and expediently, they are no longer required to apply a fix. Users can disable studies.
"The recommended course of action for those users still affected will be to update to Firefox 66.0.5 when it's available today (Tuesday US time) on Desktop and Android when it is available. A user can manually update to 66.0.4, but may need to re-install add-ons (66.0.5 addresses this, where the update will not require any re-installation)."