I, and people I know say it like "groSHery". There could be regional differences.

Hi July There are various pronunciations. In my southern English accent I pronounce 'grocery' with 3 syllables so that it sounds like 'gro-sir-ry'. However, there are some American accents (and maybe British ones too) that pronounce ;grocery' with just two syllables like 'gros-ry'. I don't think I have ever heard any native speaker say 'grocery' with a /ʃ/ (sh) sound in the middle. Here is a video with the 3 syllable pronunciation. https://www.youtube.com/watch?v=JldwYh5BvGs I hope that helps! Greg

The US is a very big country. In my corner of the country (NW US), I've never heard anyone say "groshry." Around here that would be very, very odd.

Groshry is very common in my part of the U.S. It's how I say it. This is one of those pronunciations that varies from place to place. It's not considered ignorant or incorrect. The comparison with 'libary' is a false one. That is considered incorrect in all cases.

Never heard it pronounced with an 'sh' sound either. That's definitely not how it's pronounced in the UK, regardless of region. I can't speak for the United States.