I actually like playing against opponents who attempt to play the same way that I play with their color.
The important part however is to not follow your favorite lines to the very end. As you said, there is a reason you consider them worthwhile. Instead, use your knowledge about which moves you consider unpleasant when playing that variation. Chances are that your opponent, who apparently likes the style of a line you like, will dislike this deviation as well and will be just as uncomfortable as you. Keep calm, and you might be the one with the psychological high ground.
Playing against your own weapons also is a good way of sharpening them. Best case, one of your chess buddies plays the same variation. Then both of you can play a lot of practice games against each other starting with this variation with alternating colors and test possible ways your opponent might attempt to counter your strategy. I think you learn more by literally putting yourself in the opponent's skin and really trying to find winning moves against your variation rather than by just assuming their moves while exclusively playing your own side in training, which might lead to some bias ("hopefully he'll continue with this move in this line..").