Yes, "I don't want them teaching it" is natural English. Similarly "I don't want him going there", "I don't want her seeing it", etc. etc.
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Hans51is it a short version of "I don't want them to be teaching it[no period]"?I would say no, even though their meanings are very similar. The catenative verb want is one that licenses either a to-infinitival or a gerund-participial as complement, the latter being rather informal in style.
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