@aog
Instead of flat-out prohibition, you could have a watered-down version where it is stipulated that the infant must have at least 6 sets of great grandparents, or 15 sets of great-great-grandparents, or whatever.
The ultimate limit is that you mustn't put the Royal Family into a situation where they would (or could potentially) be made into law-breakers, part way through a marriage (laws are seldom made retro-active).
Incidentally, the wiki Royal endogamy page lists Elizabeth Bowes-Lyon as a 13th cousin of her spouse, the most distant relationship on a list which goes back to pre-Norman times (other than Mrs S, who never became Royal, as such).
@beso
//The eggs cells of the female are all produced during gestation and mature later. No further division is involved in this process. //
They are still subject to however many years of exposure to dissolved substances such as ethanol, teratogens (e.g. dioxins, PCBs), medicines, recreational chemicals etc. They are well protected from non-penetrating radiation (UVA/B, alpha particles) but cosmic rays and gamma rays can pass right through living tissue,potentially leaving a trail of ions which can damage DNA or whatever biomolecules are nearest them at the time.
To be fair, some DNA damage is more likely to kill the cell completely than turn into a non-lethal - and thus heritable - gene defect but that is what sexual reproduction exists to attempt to cancel out. Some of those 'defects' turned out to be advantageous, hence variety, hence evolution.
Anyway, it's bad news for the career woman paradigm. We don't know the full ramifications of embryo cryogenics but, so far, so good.