TL;DR: There's no specific word for people who vilify or are prejudiced against other "countries". The closest general term would be bigot, but there are also terms for prejudice against certain specific nations/nationalities or ethnicities.
It's important to use the correct terms. Firstly, the term you're looking for is not "racist", since this can only be used in relation to race rather than nationality, ethnicity or "country".
Merriam-Webster defines racism as:
1: a belief that race is the primary determinant of human traits and
capacities and that racial differences produce an inherent superiority
of a particular race
2a: a doctrine or political program based on
the assumption of racism and designed to execute its principles
political or social system founded on racism
3: racial prejudice or discrimination
[Interestingly, racism is a relatively recent term. Merriam-Webster cites its first known use as 1902. That's not to say the concept or the practice didn't exist before then; M-W's dictionary entry includes two full paragraphs on "The History and Dictionary Meaning of Racism", and is worth reading].
So, is there a specific word for people who vilify, or are prejudiced against, other "countries"? The answer is no. In the absence of a specific word, the most applicable general term would be:
a person who is obstinately or intolerantly devoted to his or her
own opinions and prejudices
especially: one who regards or treats
the members of a group (such as a racial or ethnic group) with hatred
Bigot significantly pre-dates racist: M-W says the first known use was in 1660.
The term bigot shouldn't be confused with xenophobe, though no doubt there are parallels between the two. Merriam-Webster defines xenophobe as:
one unduly fearful of what is foreign and especially of people of
M-W also offers the following broader background and explanation:
Xenophobe is partly based on the Greek noun xenos, meaning "stranger,
guest, foreigner". Unlike other phobias, xenophobia isn't really
considered an abnormal condition; instead, it's generally thought of
as just serious narrow-mindedness, the kind of thinking that goes
along with racism and extreme patriotism. In times of war, a
government will often actually try to turn all its citizens into
Lastly, there are many words that define a fear, aversion or hatred of a specific nationality, ethnicity or cultural identity. These words are most easily formed with the either the prefix anti- (e.g. anti-American, anti-Semite) or the suffix -phobe (e.g. Anglophobe, Francophobe, Islamophobe). Wikipedia provides a comprehensive list of anti-cultural, anti-national, and anti-ethnic terms.