3.5 as a system has a lot of flaws, and few advantages – enormous selection of material is the biggest one
If you are not taking advantage of the enormous selection of material available in 3.5 (and the flexibility of the system, which allows you to use that material, between feats, multiclassing, and so on), I would argue that you are missing out on one of the few things that 3.5 legitimately does better than other, similar systems. If you don’t want all that material, you would be better served by using a different system that works better – which could be 4th or 5th edition, Dungeon World, or even something completely different like Fate.
Furthermore, it’s not as if Wizards consistently made one setting more powerful than another – they were supposed to all be workable together. And that more-or-less actually happened, though mostly because even the core books have wildly differing power levels depending on the choices that you make. In fact, just about every other book has less variability than core does.
So there’s a good, systemic reason to be fairly accommodating, in terms of material allowed, and limited mechanical reason to avoid the material from specific settings. Furthermore, the overwhelming majority of setting-specific options are really rather generic, they just happened to be printed in a setting-specific book. That does not mean you should just allow everything – certain, specific options may be problematic. For example, Forgotten Realms may not be higher-power in general, but the incantatrix prestige class from Player’s Guide to Faerûn certainly is much higher-power than typical. Or, as in your example, the Shadow Weave feat depends an awful lot on specific features of the Forgotten Realms, which would be awkward or problematic to include in other settings.
Most material from setting-specific books isn’t really a problem. Some of it can be, either because it’s poorly-designed (though that happens plenty in non-setting-specific books, too), or because it is really specific to the setting it comes from. I strongly recommend generally allowing material from other settings, but reserving the right to ban certain things for reasons of either mechanics or fit.
The tinker gnome, though, I don’t see as all that problematic. Fluff-wise, they’re just gnomes that are a little more creative, not that the default gnomes are falling short in that regard. The tinker gnome doesn’t even have to be treated as a separate race, they can just be special or aberrant gnomes. Mechanically, the default gnome gets a +1 bonus to the DCs of Illusion spells, which tinker gnomes don’t get: the +2 Intelligence provides a broader bonus, but since your concern was primarily Illusion spell DCs, note that the core option would have been just as good in that regard. Furthermore, gray elves are a core race that gets the same +2 Intelligence. Tinker gnomes are better than gray elves in general, but not massively so; generally speaking, humans make better beguilers than do tinker gnomes anyway. Bonus feats are huge.
So yeah, personally: yes in general, but sometimes no to specifics: for example, no to Shadow Weave, but I’d allow the tinker gnome.