Given Harry had already experienced his relationships ending (if reporting was correct) over the complications of marrying into the RF and the amount of scrutiny it brought, and having been aware of the amount of shit that Diana, Fergie, and Kate all got from the press, it is completely unfathomable to me that he didn't prepare her. Women marrying into the RF get enough shit from the press generally, let alone when she's a biracial, American actress. It was a massive failing on his part.
Harry had also seen the Yorks have their security removed back in 2011(?), so why he would possibly think Archie would be entitled to security, I don't know.
However exceptions were made for Charlotte and Louis, to ensure that they were titled pretty much from birth. It seems that such exceptions would not be made for Archie, for whatever reason. MM saw this in the context of "discussions and concerns" about the colour of Archie's skin.
I feel like I'm repeating myself on every thread about this but it's clear it's not well known. Leaving everything else aside, there were actual reasons behind the change for William's children and it was due to the Succession Act 2013 which allowed his firstborn child to be his heir, even if female. Because the Letters Patent 1917 allowed the 'eldest son of the eldest son of the Prince of Wales' to be HRH Prince, there was a risk that William would have one or more daughters that outranked a younger son in terms of line of succession, but that were outranked by their younger brother in title (they wouldn't be HRH until Charles ascended the throne but the eldest male child would be from birth). That would cause issues in terms of status that, until now, wouldn't have been possible due to the male primogeniture rules. It didn't make sense. They couldn't know in advance how many girls William would have so made it a rule across the board for William's children so as not to have only the youngest male children of the direct heir to be lower in status than his older brother and sisters. That's why it was necessary to make the change for Charlotte and Louis, it was done for all of them before George was even born. The same need isn't there for Archie as a child so far away from the throne. If you read the various laws it does make sense.
Frankly, even without all of that, as the son of the heir's heir's brother, Archie simply isn't as important in terms of 'being royal' as his cousins (not to be confused with his equal importance within the family more generally), so there is little reason to treat them equally. Given the whole institution is based on some people being more important than others due to the circumstances of their parentage and birth order, I don't actually see a problem with discrepancies in title. It's not the same as treating them equally in terms of their place in the family as a family (rather than as royalty).
Of course, if you were already feeling pushed out and hated I don't doubt it's an easy thing to pick up on and think it's to do with race, especially if there were previous 'concerns', but there's a pretty rational explanation that would have applied regardless of who Harry married.
As for a change in law so he can't get it in future, I imagine that would have been on the cards anyway as part of Charles 'slimming down' of the royals anyway. Stripping the Yorks of their titles to 'even things out' would be significantly more of a statement than saying that from now on, unless you're born into the direct line of succession you don't get a title, but he'd already taken away the Yorks' security and it wasn't any secret Queen had always expected them to go and get normal jobs rather than being fully active working royals, so in terms of that entitlement, it should have been pretty obvious the same position would be applied.