I remember seeing such a comment on Twitter long time ago but I see so many prominent papers doing it that I doubt it can really bad. Does somebody know more (e.g. papers) on this?
Is matching combined with Diff-in-Diff a bad idea?
But, as with anything, it depends on the context. One point to consider is that you should match on pre-treatment characteristics, because treatment can affect the variables used for matching.
All usual caveats of both approaches still apply, but I'm not aware of any literature diving deep into this combination per se.