So... what is safe to use these days? The NES operative system? Or did the hackers went back in time and retroatively hacked nintendo too.
I'm fairly certain there's a couple (read: too many to count) of exploits that would allow you to break the 2A03 in that thing. It's a 6502 CPU in there, anyway, so I'm sure you could have some fun with that. Just look at the NES demoscene. (Then again, the NES demoscene isn't quite as developed as, say, the C64 demoscene, so it's not as impressive in my eyes)
There was that lockout chip, the 10NES, but that's already been fully-reverse engineered, and people have made clone chips (most famously, Tengen with their Rabbit chip) that pretend to be a working 10NES chip on the cartridge side to bypass the lockout entirely.
Like, your best bet is to use Tails (Tails is a Live-USB-only distro, and that's by design). It's Linux-based, so you'd have a hard time trying to get viruses by accident. Do not save anything onto the Tails disk, if you wanna be extra paranoid. Oh, and I guess use a Ryzen PRO CPU, since Ryzen has fewer vulnerabilities than Intel. The PRO part is needed if you really wanna be secure; there's some extra security features in the PRO variants. Update your BIOS regularly, since it contains security patches for the microcode. And, of course, follow standard safety procedures for the Internet: don't be a dumbass, don't share your personal details if you're dubious, use long passwords...
I'm sure there's more things you can do if you really want to crank up the security level, but I think that's most of it.