"Hope everything goes well" is about something happening now and wishing for the consequences and results to turn positive soon. "Hope everything is going well" is about the current situation and hoping that the circumstances are fine and everything is happening in a pleasant manner at the present time.

hope everything goes well - this refers to a time in the future. hope everything is going well - this is the present tense.

To my friends I would use either and mean now. But Hayley is right.