Many parents will be more worried about than in opposition to your transition. Sometimes this worry comes out harshly. Mention that this was not a decision you made capriciously. Point out that you are working with qualified professionals in making this transition. If disclosing to a father, I would suggest you also reassure him that you have a secure job.
Fathers tend to worry about work issues.
I resolved not to disclose to my parents until after I handled disclosure on the job. As it happened, I disclosed in the same week. In other words, do everything you can to reduce their worry. By this I mean, tell them just what they need to know to understand your situation. Give the broad strokes at first, fill in the details later.