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

SearchView consists of different views, which can be - and in this case should be - addressed individually. If you want your SearchView (v7 support) to freeze and sit in that state without responding to any 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);
(Also, I had a problem with the deeptis answer searchView.setInputType searchView.setInputType(InputType.TYPE_NULL) : if you disable SearchView this way and then click on it, the system seems to expect an open keyboard, although the keyboard does not appear. Therefore, the first return button click causes nothing but closing — not shown or not open — the keyboard.)
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