A vaccine that protects you from one thing can make you more vulnerable to another.
I think you are confusing viral interference and vaccine enhanced susceptibility and making hash out of it.
Vaccines do not make you susceptible to other diseases, but have been known to enhance susceptibility to the target virus rather than create immunity to it. There is also the problem of “hot” batches where the virus was not killed/weakened sufficiently thereby causing the disease instead of inducing immune response.
mRNA vaccines are intended to sidestep both issues because they do not contain actual virus.