Twitter, prompted by the rapid spread of alternative narratives, started actively warning users about the spread of COVID-19 misinformation. This form of soft moderation comes in two forms: as an interstitial cover before the Tweet is displayed to the user or as a contextual tag displayed below the Tweet. We conducted a 319-participants study with both verified and misleading Tweets covered or tagged with the COVID-19 misinformation warnings to investigate how Twitter users perceive the accuracy of COVID-19 vaccine content on Twitter. The results suggest that the interstitial covers work, but not the contextual tags, in reducing the perceived accuracy of COVID-19 misinformation. Soft moderation is known to create so-called ”belief echoes” where the warnings echo back, instead of dispelling, preexisting beliefs about morally-charged topics. We found that such “belief echoes” do exist among Twitter users in relationship to the perceived safety and efficacy of the COVID-19 vaccine as well as the vaccination hesitancy for themselves and their children. These “belief echoes” manifested as skepticism of adequate COVID-19 immunization particularly among Republicans and Independents as well as female Twitter users. Surprisingly, we found that the belief echoes are strong enough to preclude adult Twitter users to receive the COVID-19 vaccine regardless of their education level.