Yes, which suggests that there's pretty much no-one who can't have an mRNA vaccine.
I'm not sure what they mean by "live" vaccine, since usually the vaccines are "attenuated", that is based on a live one but either killed or adapted so can't spread.
CSL had a problem with the Japanese encaphalitis vaccine around 1990 where the live vaccine wasn't actually attenuated (i.e., they hadn't actually killed it), so it was viable and people actually got encephalitis.

