It's a huge problem. There is no other fifth gen option available to NATO. The Gripen is one of the best choices out there, and it does have a lot of stealth and EWAR capabilities that other fighters lack, as well as really impressive radar, but that's not the same thing as the kind of stealth that the F-35 and F-22 have.
On the other hand, I can absolutely see how the F-35 now presents an unacceptable security risk.
The good news is that Russia has nothing even close to the F-35, and its honestly unlikely that most of their stuff can even stand up to the Gripen. Their purported fifth gen fighter just isn't. It has a radar cross section over a thousand times larger than that of any US fifth gen, that's according to Russia's bullshit propaganda numbers. And they've only made about 6 of those. The rest of their fleet is slightly upgraded cold war surplus, maybe at the level of the F-16 if you're being really generous, and the Gripen wipes the floor with the F-16 in combat testing (Gripen pilots shoot down F-16s at a ten to one ratio IIRC).
If we assume that Russia is the main threat, then the Gripen will serve very well for now (at least for Canada, with no need for a carrier launch capability) until we can get a sixth gen fighter; Europe has two such projects in the works. If we assume the main threat is the US, then the F-35 would still be a bad idea, since even putting aside any issues with supply of firmware, they would know its capabilities and weaknesses intimately. China is the wildcard and we just don't know what the capabilities of their craft are. OTOH its extremely unlikely that there would be a conflict with China that didn't involve the US as the primary combatant, so I think that's less of a concern for the rest of NATO.