No, their concern was specifically over mRNA and how it might screw with the body.
Over 2021 and 2022 it very much felt like the pro-vaccine crowd was the anti-science crowd: While they were dismissing all concerns with things like the overly-simplistic "that's not how it works, it's DNA -> RNA -> proteins like we learned in school", the MAGA crowd was talking about reverse-transcriptase enzymes and sharing studies like https://www.mdpi.com/1467-3045/44/3/73
Their concerns were never addressed, just ignored. It's not surprising they stopped trusting authorities like the CDC.
Over 2021 and 2022 it very much felt like the pro-vaccine crowd was the anti-science crowd: While they were dismissing all concerns with things like the overly-simplistic "that's not how it works, it's DNA -> RNA -> proteins like we learned in school", the MAGA crowd was talking about reverse-transcriptase enzymes and sharing studies like https://www.mdpi.com/1467-3045/44/3/73
Their concerns were never addressed, just ignored. It's not surprising they stopped trusting authorities like the CDC.