None of the stated answers were sufficient for my needs, so I would like to provide another one for anybody in the same situation.

A SearchView is made up of different Views, which can be - and in this case have to be - addressed individually.
If you want your SearchView (support v7) to freeze and grey out in a state like this, not answering to any kind of input, including the search and clear button, you can use:
ImageView clearButton = (ImageView) searchView.findViewById(android.support.v7.appcompat.R.id.search_close_btn);
SearchView.SearchAutoComplete searchEditText = (SearchView.SearchAutoComplete) searchView.findViewById(android.support.v7.appcompat.R.id.search_src_text);
clearButton.setEnabled(false);
searchEditText.setEnabled(false);
searchView.setSubmitButtonEnabled(false);
( Besides, I got an issue with deeptis answer searchView.setInputType(InputType.TYPE_NULL)
: If you disable the SearchView this way and click it afterwards, the system seemingly expects an open keyboard though the keyboard isn't shown. Therefore, the first back button click causes nothing but closing the - not shown or not in fact opened - keyboard. )