> I think duplicating the whole body of functions is not better
> than using advice.

Until yesterday, I had no idea how to advise a function.

Now I'm experimenting with this code to obtain modified versions of 
|occur| and |how-many| that are sensitive to |isearch-filter-predicate|.

I'm not a programmer, so my code may not be very rigorous:

;; I need a copy of `re-search-forward' because it will be temporary 
adviced in
;; `how-many-ifp' and `occur-ifp' functions:
(defalias 're-search-forward-copy
   (symbol-function 're-search-forward)
   "Copy of `re-search-forward'")

(defun re-search-forward-ifp (REGEXP &optional BOUND NOERROR COUNT)
   "Modified version of `search-forward-regexp' that filters (skips) matches
according to `isearch-filter-predicate'."
   (let ((POINT (point)))
     (catch 'filtered
       (while (re-search-forward-copy REGEXP BOUND NOERROR COUNT)
         (let ((B (match-beginning 0))
               (E (match-end 0)))
           (when (funcall isearch-filter-predicate B E)
             (throw 'filtered (point)))))
       (goto-char POINT)
       nil)))
(defalias 'search-forward-regexp-ifp 're-search-forward-ifp)

(defun override-re-search-forward (orig-fun &rest args)
   "Temporary advice the `re-search-forward' function, overriding it with
`re-search-forward-ifp' to make it sensitive to `isearch-filter-predicate'"
   (unwind-protect
       (progn
         (advice-add 're-search-forward :override #'re-search-forward-ifp)
         (apply orig-fun args))
     (advice-remove 're-search-forward #'re-search-forward-ifp)))

(defalias 'how-many-ifp
   (symbol-function 'how-many)
   "Copy of the `how-many' function (to be) adviced to obey to
`isearch-filter-predicate'")
(defalias 'count-matches-ifp 'how-many-ifp)

(advice-add 'how-many-ifp :around #'override-re-search-forward)

(defalias 'occur-ifp
   (symbol-function 'occur)
   "Copy of the `occur' function (to be) adviced to obey to
  `isearch-filter-predicate'")

(advice-add 'occur-ifp :around #'override-re-search-forward)

The key is the `re-search-forward` function used in `how-many` and 
`occur` definition. If you make it sensible to 
`isearch-filter-predicate` also `how-many` and `occur` will be.

I don't know if advicing a function to advice a function inside it is a 
good idea but it seem to work (I need more tests).

Now I discovered how to build these functions I could be fine with my 
modified ones, but making this feature avaible (maybe not default) in 
the original functions could be a better idea.

>   An alternative would be to add a new variable
> 're-search-forward-function' and then to use it like
> '(funcall re-search-forward-function)'.

The idea of a new function seems good to me.