Private User - I recall pointing out many, many years ago that Geni's phrasing about Privacy and only those in your family being able to see and edit the private profiles in your Max Family was not actually accurate - for example that the Max Family of your 3rd cousin likely included folks not in your Max Family. Sorry you are suddenly tripping over this.
However - one comment and then a suggestion. Among my relatives, we seem all agreed that the person who is more closely related is to be the one whose wishes will be followed when we differ not on facts, but on how something should be listed.
Suggestion if you have not tried it: Send a PM to this person, mentioning that is your parent and you very much prefer only the year to be shown in the Birth Date - he is probably working away from records and may very well not have realized that year-only was a serious preference of the person's child rather than due to lack of exact knowledge. You also might consider whether you are willing to have the full date documented in the Timeline Event and/or About or you do not want it shown at all, and explain that in your PM.
If you have not explicitly said such, then blocking him for that action is also probably a bit unfair. Strongly suggest try communicating first. Then if he angrily rejects and keeps changing it, blocking may be justified.