I am Roman Catholic...when I go into my friends Jewish home can I touch the mezuzdah as I enter his front door?

Shalom, Thank you for your question. Yes, you may touch the mezuzah case as you enter your friends house as a sign of respect. This is not an obligation (even for a Jew) but rather a custom of respect, and to recall that G-d is with us when we enter and leave our houses. Let me thank you for your concern and respect of the Jewish people and our religion. It is lovely to see a mutual honor between peoples. May we all merit to see a world of peace and love, with the blessings of L-rd to all. Blessings.