I don't want to marginalise your concerns, but can you give an example how exactly the data included in this survey could (with non-negligible probability) be abused?
For instance, forcibly "outing" an atheist in an unfriendly community.
Perhaps more importantly: if people do not have the presumption of anonymity when they fill out a survey, then survey results in general become more unreliable. There's been plenty of work done on how self-reports change when the people filling them out know they'll be viewed by people in their out-group and/or in-group.
If your concern is that there is too little data in the survey to identify individual members, I would direct you to gwern's essay on The Tragedy of Light.
The results for these have been stable for a while now; I'm posting them a bit late. 95 people took the survey after I modified it to add two questions. For the public version, I removed the pre-change data (10 data points).
One text response included identifying information, which I removed in the public version of the data. If you participated and there is any information you provided that you would like removed from the public version, PLEASE tell me as soon as possible and I will remove it.
P.S. To the person who predicted an 80-90% significant difference between different parts of California: I predict with at least 90% confidence that there will be no significant difference, because of the wide spread of locations and smallish sample size of this survey.
(The original post about the survey.)
EDIT: After some comments that it was unethical for me to post the data (in particular the text), I removed public access from the link provided earlier. Given my precommitment to post the data, I assumed it was clear enough to respondents that it would be public. I'm not convinced that this has hurt anyone, but given that others seem to disagree, it seemed prudent to remove it. Please feel free to continue this discussion; I'm interested in your thoughts.