Issues with publishing dissertation on an interest/advocacy group's website
I would be cautious. That said, I think there are easy alternatives that don't involve giving up exposure of your work through their advocacy.

If you value credibility as an independent researcher, you will be well served by not being perceived as shilling for any particular organization or political cause. I think the interests of the organization that is requesting permission to republish your dissertation is in line with this. If your research is findings that are politically expedient for them, they benefit from the enhanced credibility that you garner from perceived intellectual independence.

My advice would be something like this:


Publish your dissertation on your own website or in your institutional archive. (If you don't have a website, now would be a great time to set one up!) It should only take a day or so to get set up.
Once you've done that, suggest that the organization write a summary of your work on their website — clearly in their voice — and to link to or repost (if they feel that is absolutely necessary) your work.


You will benefit from the traffic to your website and they will benefit by having your work seem like the work of an independent researcher and not something done by someone inside. And indeed, it sounds like this is exactly the case!