It isn't just FFLs. The Gun Control Act (GCA) defines a list of people who aren't allowed to ship, transport, receive, or possess firearms of ammo. This includes any person "who is an unlawful user of or addicted to any controlled substance (as defined in section 102 of the Controlled Substances Act, codified at 21 U.S.C. § 802);" [1]. Since cannabis is federally illegal still if you use it you can't legally even possess (not just own) a firearm or ammo.
I think it is a stupid law though. Imagine if we applied that logic to other constitutionally protected rights. "Anyone who is an unlawful user of or addicted to any controlled substance shall not have the right to vote" or "Anyone who is an unlawful user of or addicted to any controlled substance shall not have the right to due process".
Admittedly, it's hard to kill another person by voting, or receiving due process. And we do restrict speech when it verges on violence (imminent lawless action, fighting words).
> "Anyone who is an unlawful user of or addicted to any controlled substance shall not have the right to vote" or "Anyone who is an unlawful user of or addicted to any controlled substance shall not have the right to due process".
Not the same thing at all, because a firearm is directly and irrevocably more dangerous while under the influence of drugs.
You can debate the tradeoff of "right to bear arms" vs "right to regulate arms" (just as voting has gone through lots of regulations, some terrible (black people, women), some OK or debatable (showing proof residence or citizenship somewhere in the process), but it's not obvious simply by analogy to other rights.
I think it is a stupid law though. Imagine if we applied that logic to other constitutionally protected rights. "Anyone who is an unlawful user of or addicted to any controlled substance shall not have the right to vote" or "Anyone who is an unlawful user of or addicted to any controlled substance shall not have the right to due process".
[1]https://www.atf.gov/firearms/identify-prohibited-persons