Well, it's not really a word.
If it were, it'd mean that you have an irrational fear of assimilating into a culture or society. Note, when saying irrational....it really means IRRATIONAL (in bold wording).
Most people who travel a lot....have a chance to view other societies, cultures, religions, trends, foods, beverages, landscapes, laws, acceptances, and prejudices. You might walk around and utter 'openness' while in this stage of travel and claim you are broad-minded.....although it just means while on vacation, you simply had opened your eyes....it doesn't mean you will run back to your home-country and try implementing some changes and trying to remake your own culture.
If you were assimilaphobic.....you'd grin, wave at people, walk around with a fake character.....and just refuse as the days, weeks, and months go by.....to be any different than you were on day one of arrival.
In the old country, you view cops and politicians as thugs or crooks, and you might just keep this view in your new country.
In the old country, you viewed women who wrapped themselves up to protect their virtues and sensitive nature as a good thing, and you'd like to keep this view in your new country.
In the old country, you viewed alcohol and booze as an evil, and you might want to retain this view in the new country.
In the old country, you viewed journalists as simply agents of the government, and have nothing positive to say about the journalists in the new country.
The list goes on and on.
Based on frustrations and irrational actions....you quietly go about your life in the best way possible....without any integration or assimilation. If someone wants you to take some stupid class and pass a test....fine, you can fake your way through a hundred hours and make a marginal score which makes some government guy happy enough to sign a sheet and note you were "integrated". In the end, you hold this stamped integration slip proudly, while you continue your assimilaphobic lifestyle.
The problem with this is not so much the guy who is the assimilaphobic....but rather his son or daughter....who grow up in the new land and continually have dad or mom bash the new land and keep chatting about how wonderful things were in the old land. So, twenty years down the road....you have some kid who has grown up and is utterly confused to his situation in life. He or she hasn't succeed at much in life....due to conflicts in school, a bad attitude, and inner frustrations over assimilation (it just never happened). The kid can't climb out of the neighborhood....get a decent job....or dream of anything much because he or she is locked onto the parent's perception of assimilation (or lack of such).
At some point, a mental health guy will sit down....analyze the situation, and invent the word Assimilaphobic, and try to proscribe some treatment for it. He'll get lots of time on some chat forum TV show and hype up his newest book. And people will sit there and ask if we really need to discuss this matter.