Leaving aside Vong (who are disconnected from the Force) were there any species whose members could not become Jedi even if they were Force Sensitive (too evil, or too weak in the Force, or any other reason)?
In Legends/EU, there were at least 3 who were not intelligent enough to become Jedi (though, since you don't need intelligence to be Force Sensitive, it doesn't necessarily mean they couldn't produce Force Sensitives):
There are a number of species, apparently, who either lack the ability to use the Force, or who lack the subtlety of thought necessary for Jedi training. Back when I was writing the Jedi Council series, I'd wanted to have a Jedi character of the same species as pod racer Dud Bolt (I can't remember the name of the species off-hand), but I was told that they're not smart enough to be Jedi. (So, I settled on whatever species Ratts Tyrell is. And that's how Jedi Master Tsui Choi was born.) anyway, the Tuskens, I've been told, aren't smart enough to use the Force. Neither are the Ewoks (sorry, Matt).
Tuskens (as per above)
Please note that "Tusken Jedi" Hett was actually a human.
One Ewok Jedi slipped in from earlier EU canon, before this judgement of Ewoks could be pronounced to Randy. Since it contradicts the later LuasFilm canon rules, would make the Jedi Ewok fact S- or N- canon, as per EU rules.