It doesn't much matter if you use who or that.
But there are several other mistakes in your sentence, so for the benefit of space I post this as an answer.
The main problem with your sentence (which is a question and deserves a question mark) is that consider to become member does not make sense. You can be considering membership of the EBU, or considering becoming a member. But it is not idiomatic for a country to consider to become a member.
You would in any case need the plural verb consider (rather than considers) to agree with countries.
And member either needs an indefinite article -if singular, but to agree with countries it really needs to be plural. So in all:
What are the main prospects and challenges for non-euro-area countries that are considering membership of the European Banking Union ?