There is always influence. One can never separate it and become a truly, wholly non-influenced person, society, or country. Muslim traders in the 1400s spread their religion throughout Southeast Asia because they wanted to influence their customers, and customers converted because they wanted better deals from those who would deem them of a similar faith. That is the same process here. If a country doesn't like such influence, such as Japan with the Dutch, they can ban it.
On the flip side of the coin, one of the most vocal opponents to repeal has been the Singapore branch of the Christian American organisation Focus of the Family [1], which counts the current Singapore foreign minister (among other politicians) as one of its patrons [2].
I don't think organisations can avoid foreign influence these days, but it'll be absurd to think that only one side was affected by it.
Indeed, just because a country wants to close down does not mean they will be successful at doing so. That is also a part of influence, when influence turns into violence.
