The vaccines do not modify your immune system, they effectively trigger memory and normal tools that your body uses to identify pathogens, viruses and bacteria, but it is not a “modification” to how your immune system works and has no impact on other pathogens. It’s not going to weaken anyone’s response to TB or any other pathogen.
If more people get it, then the virus will modify itself inside those persons, and also animals, and there will need to be surveillance for those modifications just like we have surveillance for new strains of the flu. If we can get hers immunity high, not through sickness because that does not create strong immunity, but through vaccinations, then that will slow the mutation rate, and over time we’ll have fewer mutations.
It’s when people do not do vaccinations and come up with unscientific theories that, for instance, deadly and highly transmissible diseases like measles come back and kill people.