(idiomatic) Timid, sanctimonious, or easily offended.
Example: 2007, Amanda Marcotte, It's a Jungle Out There: The Feminist Survival Guide to Politically Inhospitable Environments, Seal Press (2007), ISBN 9781580052269, page 141:
When John Kerry â€œoutedâ€ Mary Cheney in a 2004 presidential debate, it was already well known that Mary Cheney was a lesbian. You can't out the already out, no matter what pearl-clutching pundits would have you believe.
2010, April Winchell, Regretsy: Where DIY Meets WTF, Villard Books (2010), ISBN 9780345523181, page 131:
Even the biggest doe-eyed, pearl-clutching Etsy muffin has to find some way to make it okay to be negative, because we have no choice.
2013, The Best American Comics 2013, (eds. Jeff Smith, Jessica Abel, & Matt Madden), Houghton Mifflin (2013), ISBN 9780547995465, page 362:
There's something truly irresistible about the pearl-clutching cartoons that came out during the time people thought women on bicycles were single-handedly going to bring society to ruin.
For more examples of usage of this term, see Citations:pearl-clutching.