They are largely regarded as legitimate by those who study and use them (including myself), but as /u/The_Alaskan said, they need to be taken with a grain of salt. Depending on the time and date of the interview as well as the race or gender of the interviewer, the responses given by the interviewee are going to be different. In my own research as a white male, I know that when I interview an African-American, their responses would be different if another African-American were interviewing them. The same issues applied to the WPA Narratives.

I regard them as legitimate sources, with the caveat that like all after-the-fact accounts, you have to take them with a grain of salt and support them with sources taken from the moment.