Effects of mass anti-vaccines

So I'm from the UK but have seen articles stating that Trump is planning to get rid of childhood vaccines? This seems absolutely crazy to other countries (but unfortunately eggs on some conspiracy theorists!)

Anyway, away from politics I want to understand the impact of mass vaccine shunning. It scares me that people will be travelling and spreading illnesses people worked hard to eradicate, will this affect children worldwide due to a large and influential country rolling this out?

EDIT Thanks to all for answering, I know you're at a pretty tense time politically, so I appreciate taking the time to help educate us on the situation.