I've attached an updated patch.

This one has a test where we actually don't sort tags by using the
`ignore' function.

Ihor Radchenko <yantar92@posteo.net> writes:

>> +        ;; Sorting doesn't care about `org-tag-alist'.  This is only
>> +        ;; here for later when we add sorting methods that do
>> ....
>
> Then, please refrain from setting alist in this patch and add it later,
> when testing the relevant methods.

Done.  Now my tag names don't really make sense but I suppose that's not
a big issue.

>> +    (org-test-agenda-with-agenda
>> +     (string-join
>> +      '("* TODO group_a :group_a:"
>> +        "* TODO tag_a_1 :tag_a_1:"
>> +        "* TODO tag_a_2 :tag_a_2:"
>> +        "* TODO tag_b_1 :tag_b_1:"
>> +        "* TODO tag_b_2 :tag_b_2:"
>> +        "* TODO groupless :groupless:"
>> +        "* TODO lonely :lonely:")
>> +      "\n")
>> +     (dolist (org-tags-sort-function '(nil org-string< org-string>))
>> +       (should
>> +        (string-equal
>> +         (progn
>> +           (org-agenda nil "f")
>> +           (substring-no-properties (buffer-string)))
>> +         (pcase org-tags-sort-function
>> +           ;; TODO: a value of `nil' sorts it!  That's not what the
>> +           ;; customize menu of `org-tags-sort-function' says!  It
>> +           ;; says "No sorting".
>
> Right. When sort function is not set agenda specifically (but not other
> users of org-tags-sort-function) falls back to alphabetical sorting.

As far as I can tell the only place where it doesn't fall back is in
`org-set-tags'.

> In fact, the docstring does not at all mention that
> `org-tags-sort-function' is honored at all:
>
>   (defcustom org-agenda-sorting-strategy ...
>     ...
>     tag-up             Sort alphabetically by last tag, A-Z.
>     tag-down           Sort alphabetically by last tag, Z-A.
>
> We need to fix this docstring documenting `org-tags-sort-function', I think.

I don't understand what is happening in `org-entries-lessp' or how it
even manages to use `org-agenda-sorting-strategy' so I'm going to
refrain from trying to document things I don't understand.

>> +           ((or 'nil 'org-string<)
>> +            "group_a\ngroupless\nlonely\ntag_a_1\ntag_a_2\ntag_b_1\ntag_b_2\n")
>> +           ('org-string>
>> +            "tag_b_2\ntag_b_1\ntag_a_2\ntag_a_1\nlonely\ngroupless\ngroup_a\n"))))))))
>
> Nitpick: it would be more readable to use `string-join' here as well.

Done