But what if I encounter an Invariant Section saying that Social Security is wrong and that old or diseased people should be left alone and not helped by a public service? If I cannot remove this political statement, I cannot really regard the manual as free. And I would not want to distribute such statement, if I produce a modified version of the documentation.
I disagree with those statements, and I would think twice about redistributing a manual in which the author says those things. At the same time, I don't think this would mean that said manual is non-free. They are different issues. Free documentation, like free software, refers to specific freedoms. It doesn't mean that you can do absolutely whatever you want to do. (No free software license allows that; some come pretty close, but those are not the ones I recommend.) It means you can redistribute the work, change it (functionally), and redistribute modified versions. It is ok to have requirements on how you can do this, provided they don't prevent you from substantively making the functional changes you want to make. There are free software licenses that have restrictions that I find annoying and inconvenient. One is the old BSD license. I worked for several years to convince Berkeley to remove the advertising clause, which I called "obnoxious." If the Ku Klux Klan or George Dubya Bush had released a program with the old BSD advertising requirement, I might have thought twice about using it, because I would not want to advertise them. But it is still a free software license.