I think you can back them up, you just can't play them. But my memory is a little rusty since I never had the need to do so.
Nah. Super FX carts tend to confuse the living hell out of most backup units it seems. Don't quote me on this, but I think I managed to get my dumper to recognize 8mbits rom on my StarWing cart and dump it over 10 years ago by just covering the expansion pins on the cart when I inserted it, but maybe I'm just remembering things wrong and that didn't work either. (I did a lot of random stupid experiments with my dumper back in the day) Anyway, if the above turns out to be a dead end; I believe you should be perfectly able to dump SFX carts with stand alone cartridge readers (such as this one*), though I've got no clue whether or not you can rip SA-1 games (and things such as S-DD1 or SPC7110) with that thing... think those might need some special treatment (at least in the case of the SA-1) *almost sure there were some cheaper alternatives around (didn't tototek also have something like that once?)
I've heard pretty much the only thing that would dump it would be a device like the Super Wild Card DX with some kind of custom dumping software. Otherwise you have to desolder the MaskROM and manually connect it to an EPROM dumper. But there is no reason why an adapter like Tototek's or the MashMods programmer couldn't have it's software updated to be able to read these cartridges. Curious though, do you have something worth dumping? I would think anything undumped like a beta or prototype would be on a board with standard EPROMs probably socketed.
It probably has to do with bank switching. So most application or devices probably dont understand that. I came across the same difficulties with dumping an Atari Flash Cart the other week by default all preexisting methods would only dump the boot rom because of the bank switching they couldnt not understand even when providing the start addresses.
It should be possible with the Retrode adapter. Starfox is listed in the compatible games list: http://www.retrode.org/wordpress/documentation/compatible-games/ However that piece of hardware is quite expensive.
I've dumped all my Super FX games with a Mash Mods flash programmer without any issues. (I have Dirt Racer, Stunt Trax FX/Wildtrax, Yoshi's Island, Vortex, Star Fox, Super Star Fox Weekend). The Mash Mods programmer can dump any snes game, except for those over 32 Mb, SA-1, SDD-1 and S-RTC games. I haven't tried Capcom chips, though. Super FX and DSP-x games are dumpable.
ASSEMbler, there was some guide on the tototek forums how to do this, I did it in the past and successfully dumped a few SuperFX carts with the Tototek adapter.