Social psychological researcher here. This is interesting enough to merit further research, but as the researcher is quoted, and others have vaguely mentioned, there are a lot of control flaws:

1) They only used one fictitious female name, but should use many. This is important for establishing that the effect occurs for female names in general, not a specific name. I don't live in Texas, but perhaps Ferris is a name that carries political connotations. Personally, I think of Ferris Bueller's Day Off, which is a bias in itself--those rebellious kids trying to take advantage of the system!

2) They didn't have a set of fictitious male names to use as controls. This would be important for establishing that the effect isn't a general distrust of strangers, but specifically to female unknown names.

3) Really they should test this with both Democrats and Republicans. I don't see the point in targeting Republicans except that it is likely easier to survey Republicans in Texas, since there are more of them around. Still, the effect may span political parties.

4) They should show differences in the effect for male and female voters. If I had to hypothesize, an anti-female bias would be a little bit stronger among male voters, but would also be pretty strong among female voters. Still, this would be important to show.

As others mentioned, too, similar effects have been shown with racially-related and gender-specific names in employment research. There are also biases against overweight and homosexual individuals in hiring. Interestingly, hiring biases sometimes don't express until the interview stage. For example, many people will rate homosexual and 'strait' people's resumes the same, and offer interviews to them at the same rate, but they will end up treating them very differently in the interview stage.