Introducing new ideas and replacing old ones is/are always a highly controversial matter, especially when there is already tension between an older and a younger generation.
Thank you Thai Pham
Top answer
are
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are
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If you use "are" then I would also recommend changing "a ... matter" to "matters," but I don't like that much
You can argue that "introducing new ideas" and "replacing old ones" are actually one joint subject, and keep is, but I don't really like that much either.
Sometimes you have to rewrite to be both correct and natural: It's always highly controvertial to introduce... and