Not "cannot" but "may not" -- a non-Jew or a not-yet-converted candidate is not allowed (under Jewish law) to abide by all the laws of the sabbath (sometimes, a candidate is told to turn a light on once per sabbath, or carry something in his pocket (in the absence of an eiruv).)
Ah. Good comparison example, if you are familiar with Catholicism.
Any Christian male or female can go to Mass atna Catholic Church but they cannot take the Eucharist
Once the male Christian is converted to Catholicism, he, then, can take thr Eucharist.
However, although the female and male converted Catholic can take the Eucharist, only males (because of the line from Peter all males) can be priest and take on that vocation.
Females can give out the Eucharist (as non-jews may observe the Sabbath) but she cannot be a priest and bless the Eucharist as Jesus (just as a non converted Jew may not practice the Sabbath)
So, just like the female whoncan give out the Eucharist so can a Jew so work (for?) converted Jews who, by their laws, are prohibited from working on the Sabbath.
Did I get the comparison right?