Those that clog up hospitals are usually people with health conditions and comorbidities. There’s never 100% immunity rendered from the vaccine either and vaccinated people can also have breakthrough infections.

They can get sick with Delta and spread it to others just as easily as unvaccinated. When there was an outbreak in Boston, 74% of people were fully vaccinated. Read about it here: https://www.cnbc.com/2021/07/30/cdc-study-shows-74percent-of-people-infected-in-massachusetts-covid-outbreak-were-fully-vaccinated.html

If an unvaccinated person follows all the safety measures and wears masks, they can still protect themselves and others from getting sick with Delta.