Let's say you're staying at a non-Jewish relative's house. He bought you kosher food because he knows you keep kosher. He buys you a drink such as milk. You see him pour the drink for himself into his own non-kosher glass. While pouring, the jug's spout touches his glass. Are you allowed to use that jug to drink out of?
As long as the glass is clean, yes, absolutely. You can even drink from one of his non-kosher glasses.
You can use a non-kosher vessel for kosher food, with the following conditions:
- The vessel is completely clean
- The vessel and food are both cold (less than ~113 degrees Farenheit).
- We're talking about a bowl, plate, or cup; cutting or puncturing with a non-kosher knife or fork gets more complicated -- the rules here are for standard temperature and pressure.
- The food isn't a "pickling liquid" like brine, vinegar, or hard liquor. Milk, water, orange juice -- all are fine.
- Don't let the food sit in the vessel for 24 hours.
- You don't use this non-kosher vessel on a regular basis. So don't take the cup home with you, but it's okay to use when visiting there.
As long as those conditions are met, it doesn't "treif" up your kosher food.