* lisp/replace.el (replace-lax-whitespace): New defcustom.

(query-replace, query-replace-regexp, query-replace-regexp-eval)
(replace-string, replace-regexp): Mention it in docstrings.
(perform-replace, replace-highlight): Let-bind
isearch-lax-whitespace and isearch-regexp-lax-whitespace according
to the values of replace-lax-whitespace and regexp-flag.
Don't let-bind search-whitespace-regexp. 

* lisp/isearch.el (isearch-query-replace): Let-bind
replace-lax-whitespace instead of let-binding
replace-search-function and replace-re-search-function.
(isearch-lazy-highlight-search): Let-bind isearch-lax-whitespace
and isearch-regexp-lax-whitespace to lazy-highlight variables.
(isearch-toggle-symbol): Set isearch-regexp to nil
in isearch-word mode (like in isearch-toggle-word).

Fixes: debbugs:10885

lisp/replace.el

@@ -33,6 +33,14 @@
   :type 'boolean
   :group 'matching)
 
+(defcustom replace-lax-whitespace nil
+  "Non-nil means `query-replace' matches a sequence of whitespace chars.
+When you enter a space or spaces in the strings or regexps to be replaced,
+it will match any sequence matched by the regexp `search-whitespace-regexp'."
+  :type 'boolean
+  :group 'matching
+  :version "24.3")
+
 (defvar query-replace-history nil
   "Default history list for query-replace commands.
 See `query-replace-from-history-variable' and
@@ -226,6 +234,10 @@ letters.  \(Transferring the case pattern means that if the old text
 matched is all caps, or capitalized, then its replacement is upcased
 or capitalized.)
 
+If `replace-lax-whitespace' is non-nil, a space or spaces in the string
+to be replaced will match a sequence of whitespace chars defined by the
+regexp in `search-whitespace-regexp'.
+
 Third arg DELIMITED (prefix arg if interactive), if non-nil, means replace
 only matches surrounded by word boundaries.
 Fourth and fifth arg START and END specify the region to operate on.
@@ -270,6 +282,10 @@ pattern of the old text to the new text, if `case-replace' and
 all caps, or capitalized, then its replacement is upcased or
 capitalized.)
 
+If `replace-lax-whitespace' is non-nil, a space or spaces in the regexp
+to be replaced will match a sequence of whitespace chars defined by the
+regexp in `search-whitespace-regexp'.
+
 Third arg DELIMITED (prefix arg if interactive), if non-nil, means replace
 only matches surrounded by word boundaries.
 Fourth and fifth arg START and END specify the region to operate on.
@@ -346,6 +362,10 @@ minibuffer.
 Preserves case in each replacement if `case-replace' and `case-fold-search'
 are non-nil and REGEXP has no uppercase letters.
 
+If `replace-lax-whitespace' is non-nil, a space or spaces in the regexp
+to be replaced will match a sequence of whitespace chars defined by the
+regexp in `search-whitespace-regexp'.
+
 Third arg DELIMITED (prefix arg if interactive), if non-nil, means replace
 only matches that are surrounded by word boundaries.
 Fourth and fifth arg START and END specify the region to operate on."
@@ -437,6 +457,10 @@ are non-nil and FROM-STRING has no uppercase letters.
 \(Preserving case means that if the string matched is all caps, or capitalized,
 then its replacement is upcased or capitalized.)
 
+If `replace-lax-whitespace' is non-nil, a space or spaces in the string
+to be replaced will match a sequence of whitespace chars defined by the
+regexp in `search-whitespace-regexp'.
+
 In Transient Mark mode, if the mark is active, operate on the contents
 of the region.  Otherwise, operate from point to the end of the buffer.
 
@@ -475,6 +499,10 @@ and TO-STRING is also null.)"
 Preserve case in each match if `case-replace' and `case-fold-search'
 are non-nil and REGEXP has no uppercase letters.
 
+If `replace-lax-whitespace' is non-nil, a space or spaces in the regexp
+to be replaced will match a sequence of whitespace chars defined by the
+regexp in `search-whitespace-regexp'.
+
 In Transient Mark mode, if the mark is active, operate on the contents
 of the region.  Otherwise, operate from point to the end of the buffer.
 
@@ -1760,6 +1788,10 @@ make, or the user didn't cancel the call."
 		replace-search-function)
 	      (let ((isearch-regexp regexp-flag)
 		    (isearch-word delimited-flag)
+		    (isearch-lax-whitespace
+		     (and replace-lax-whitespace (not regexp-flag)))
+		    (isearch-regexp-lax-whitespace
+		     (and replace-lax-whitespace regexp-flag))
 		    (isearch-case-fold-search case-fold-search)
 		    (isearch-forward t))
 		(isearch-search-fun))))
@@ -2113,7 +2145,10 @@ make, or the user didn't cancel the call."
       (let ((isearch-string search-string)
 	    (isearch-regexp regexp-flag)
 	    (isearch-word delimited-flag)
-	    (search-whitespace-regexp nil)
+	    (isearch-lax-whitespace
+	     (and replace-lax-whitespace (not regexp-flag)))
+	    (isearch-regexp-lax-whitespace
+	     (and replace-lax-whitespace regexp-flag))
 	    (isearch-case-fold-search case-fold-search)
 	    (isearch-forward t)
 	    (isearch-error nil))