Thank you so much for all of your answers.
A friend is planning to chas v’Shalom marry a goy in a few months. If this takes place, (chas v’Shalom) is it permitted to give a gift, having it in mind that it is only for the Jew, and for the purpose of maintaining a connection with them?
To be honest you should not have anything to do with this marriage, not to attend it and not to give them any presents. The reason is because by giving them a present you are showing your support for their sin, which is called “machzik yidei ovdei aveira”, giving support to sin. You may choose to be very political about it, and not disclose the reason for your actions, but you should not be supporting or doing anything that encourages such sin. As a Jew loyal to Hashem, you must understand that what these people are doing, even if it is merely out of ignorance, is the very destruction of the Jewish people, and you don’t want to have any part in encouraging it.