I suspect that Anders is right, and whoever set up the Chrome extension ban just didn't think about Firefox. If they realized that you were using Firefox to get around the ban, they'd probably forbid that too (or try to, anyway).
FWIW, yes, browser extensions can be problematic from a security viewpoint, and I can see reasons for banning or heavily restricting them in some situations. That said, being able to install your own software, including a different browser, is just as problematic for the same reasons, or more so, so allowing that while banning extensions does seem inconsistent.
In any case, the real problem here seems to be the lack of communication. If the extension ban was based on an existing official policy, all employees should have been made aware of the policy; if not, such a policy should have been created and properly announced.
All that said, as the author of a Chrome / Firefox extension (SOUP), let me note that there is, or at least used to be, a real difference in the security review process between Chrome Web Store and Firefox Add-ons. Basically, the difference is that Firefox Add-ons used to have a mandatory manual security review process that all extensions had to pass before being approved, whereas Chrome Web Store only flags extensions for manual review if they fail an automated heuristic check.
Basically, my personal experience with submitting my extension to Firefox Add-ons and Chrome Web Store was more or less as follows:
Chrome Web Store: To be able to submit an extension, I had to pay a $5 registration fee. This actually ended up taking me a while, since my bank was apparently flagging the charge as potentially fraudulent and refusing to let it through. Eventually I managed to sort it out by calling my bank and having them manually allow the charge. After completing the registration process, I submitted the extension and it was (IIRC) almost immediately published, apparently having passed the automated checks.
Of course, without knowing exactly what Google's automated checks are checking for, I cannot tell for sure how good they are at catching bugs and malware. But I do know that they failed to spot the almost-XSS bug in my own extension that Mozilla's reviewer caught.
More generally, my impression is that Google is more focused on trying to make extension authors traceable and accountable (via the registration fee, which at least means they know my credit card details; although I'm sure a malicious actor could find ways around that) and on detecting deliberate malware. And they don't always seem to catch it, either. The former Firefox Add-ons review process, on the other hand, not only kept out malware but also actually tried to spot potential security holes even in well-intentioned extensions. And by manually reviewing updates to existing extensions, the Firefox Add-ons system would also thwart developer account hijacking attacks like those that have compromised several legitimate Chrome extensions recently.
Unfortunately, as Makyen pointed out in the comments below, this difference no longer exists: as of a few months ago, Firefox Add-ons has moved to a semi-automated extension review process, just like the one Chrome Web Store is using.
In the linked blog post, the change has been motivated by "the new WebExtensions API [being] less likely to cause security or stability problems for users." Unfortunately, that reasoning does not really convince me: WebExtensions — even pure content script extensions like SOUP — can do plenty of damage in the hands of a malicious actor.
Just the content script API basically gives an extension free access to every web page you visit and every password or credit card number that you type in. Sure, when you install the extension, you'll be told about the sites it may run content scripts on — but so many extensions (including ad blockers, privacy extensions, etc.) already require the ability to inject scripts on every site that few users will pay any attention to that warning, even if they understand what it means.
Just a week after the announcement linked above, two extensions with embedded bitcoin miners were already spotted on Firefox Add-ons. So it seems that, when it comes to extensions, the former security advantage of Firefox over Chrome is now just nostalgia. :(