Just a small correction here, no comment on the advice in general. I'm sure what the writer means is to change your Succession Law to Elective Law, not change your Realm Law to Feudal Contract. I assume this mistake because he's talking about inheritance, where Feudal Contract has nothing to do with inheritance.
I didn't confuse different types of law, but my mistake was a false assumption - as Veldmaarschalk rightly pointed out - that changing any law causes a general vassal loyalty-hit. Checked, it doesn't, and it made the whole logic of my argument fuzzy.
But like Brettmo mentioned, Byzantium in 1066 scenario already starts with an Elective Law (which is a Succession/Inheritance Law). As you don't have at the start any representatives of Dukas dynasty besides your son Michael as your vassal - and not much spare land either or great possibilities to expand in starting years to change the situation - it might be safer to switch into Salic Consanguinity as soon as you can (although Michael starts as the strongest vassal and inheritor, it may change - and it's game over then).
I was partly right though: there's at least one character who takes a loyalty-hit when you switch from your starting Realm Law - a Royal Prerogative - to Feudal Contract as Byzantium in 1066... and that's Michael Dukas. The rule appears to be (which I inappropriately generalized to all vassals): vassals who are ruler's children suffer a 30% loyalty drop when you change Royal Prerogative into Feudal Contract. So coupled with a Elective Law into Salic Consanguinity switch (meaning 50% loyalty hit for all vassals), Michael would end up with a 20% loyalty as a result of two changed laws. You may want to avoid that.
The motivation for changing Royal Prerogative into Feudal Contract is that the former Realm Law makes your vassals lose 1% loyalty per month and the latter would increase the loyalty by 1% per month (difference 2% (or 2 percentage points, to be exact)). The result of that switch in Byzantium 1066 case means that 8 out of 10 vassals who lose loyalty each month under Royal Prerogative law (you have 29 vassals in total) start to gain loyalty under Feudal Contract... so you end up just with 2 vassals who have issues with you purely based on personality/trait-conflict.
As an end note: problem with poor-skilled Michael Dukas, your main heir, will be difficult to solve. Michael controls 5 provinces (directly and through his vassals) and you yourself start with just 3 demesne provinces - so you can't give your second son Andronikos enough land to make him pass Michael in a succession order (both - Elective Law and Salic Consanguinity Succession Laws - prefer a character (vassal or son, accordingly) with the most land controlled).
Also when you change the inheritance law all your vassals lose 50% loyalty. But this loyalty-hit only happens with changing inheritance-laws. Changing a Realm or Religious law doesn't give your vassals a loyalty-hit.
Thank you for correcting me. It's always unfortunate to give and get flawed advice. Sorry for that.
(I also sincerely appreciate, KPJ, that you bothered to react.)