"She can dish it out, but she can't take it" -- used about a someone who is known to gossip, but gets in a huff if any own says anything about her

Which reminds me of the concluding stanza of an Ogden Nash poem (no surprise there! ) titled A Little Bit of Gossip Does Me Good:

Oh, I do love a little bit of gossip.
But for scandal or for spite there's no excuse!
To think of Mrs. Page
Telling lies about my age!
Well! Her tongue is like her morals: rather loose.
Mrs. Murgatroyd eats opium for breakfast,
And then claims I'm running after Mr. Wood.
That's the sort of vicious slander
That arouses all my dander,
But a little bit of gossip does me good.