I read the quoted section in the question as:
identification of the creator(s) [...] in any reasonable manner
i.e. the identification must be reasonable. For example, you may wish to use 16MB of Zalgo text as your pseudonym. That would likely not be considered reasonable. I don't think adding an unreasonable name requirement would be a valid way to escape the irrevocable CC licence grant (in order to get content deleted).
To your other points:
The Creative Commons FAQ section on attribution says (emphasis added):
All CC licenses require users to attribute the creator of licensed material, unless the creator has waived that requirement, not supplied a name, or asked that her name be removed. Additionally, you must retain a copyright notice, a link to the license (or to the deed), a license notice, a notice about the disclaimer of warranties, and a URI if reasonable. For versions prior to 4.0, you must also provide the title of the work. (Though it is not a requirement in 4.0, it is still recommended if one is supplied.)
CC licenses have a flexible attribution requirement, so there is not necessarily one correct way to provide attribution. The proper method for giving credit will depend on the medium and means you are using, and may be implemented in any reasonable manner.
Moving on to where and how the attribution is located:
From Can I insist on the exact placement of the attribution credit? in the same FAQ (emphasis added):
No. CC licenses allow for flexibility in the way credit is provided depending on the medium, means, and context in which a licensee is redistributing licensed material. For example, providing attribution to the creator when using licensed material in a blog post may be different than doing so in a video remix. This flexibility facilitates compliance by licensees and reduces uncertainty about different types of reuse—minimizing the risk that overly onerous and inflexible attribution requirements are simply disregarded.
and from How do I properly attribute material offered under a Creative Commons license?:
Additionally, you may satisfy the attribution requirement by providing a link to a place where the attribution information may be found.
Taking your contributions licenced to Stack Exchange Inc. under CC BY-SA as an example, this would mean a reasonable attribution would be providing your user id on a post that links to your profile, where all required information lies, at your discretion. This could include your preferred pseudonym "Israel is an Apartheid State". There is nothing in the CC terms that would allow you to choose the form of the link used.
You can find the complete legal text (expected to reflect the FAQ) at e.g. Attribution-ShareAlike 4.0 International.
Addressing your question directly in light of the above:
Does this protect me if the pseudonym I wish to use is deemed to be political, but is otherwise protected speech in my jurisdiction? For example, would a site be able to deny attribution if my requested pseudonym was "Israel is an Apartheid State"?
It protects you to the extent that the licensee has to preserve the name of the creator (among other things). How exactly that is provided is up to them.