Of course you don’t stop contact with people who are not Muslim!! Your beliefs are your beliefs and they should not stop you from interacting with your friends and family.
What a lot of new Muslims find, however, is that their new lifestyle, as a Muslim, is not always conducive with their friends who follow a Western /European lifestyle.
As a Muslim believer we will dress more conservatively/modestly, we do not drink Alcohol and we tend to not partake in a lot of the same activities that Western/European people do.
Keep in mind that It is hard for the family and friends of the new Muslim. They are confused and a little frightened by your journey to Islam. Almost certainly their idea of Muslims comes from the warped impression that the media gives. Take your steps gradually and ease them, as well as yourself, into Islam.
It’s important to keep contact with your friends and family. It’s important to let them know that you’re still you and that being a Muslim is only going to make ‘you’ that much better!
There are no rules stating we cannot befriend anyone who is not Muslim but it’s also important to remember to keep good influences in your life. As Muslims, it is our obligation to dissociate with the enemies of Islam. Although it is in your best judgement to deem who is worthy of friendship.