Can "wonder if" be followed by a subjunctive clause only?

It is correct to use the subjunctive here, and not all that uncommon. Many native speakers would also use "was". It depends somewhat on personal, regional and stylistic factors. In speech or ordinary writing, generally either sounds natural. I suppose some might find the subjunctive to sound odd or old-fashioned, or the indicative to sound inelegant or uneducated. If you want to use what native speakers would consider the most strictly "correct", as in the context of a grammar test, then it might be a safer bet to use the subjunctive. Incidentally, the past subjunctive can also be used with "whether" in similar circumstances (hat tip to tchrist in comments).

Here's a Google ngram chart for "wonder if she were" and "wonder if he were". If you look through the citations, you can find examples of these phrases being used by other English writers in comparable contexts to the ones cited in the question.