They want the prestige but don't want the rest of it - it's very obvious to most people at least in UK I've encountered - and I agree with the OP it gives them authenticity problems.
However I don't agree that the original article actually points any of this out - I think it uses a click bait title along those lines but actual article seem to me just to be very sneering about Meghan's family origins and about her daring to have ambitions - it's more jumping on a bandwagon to be snobby than anything new or inciteful about Meghan,
I'm not a big fan of RF - their ancestors are the people who subjugated. exploited and killed many of my families Irish, Welsh and English ancestors but until the republican movement picks up considerable steam it's what we have and the half in half out - all the prestige and none of the downsides snipping from the sides - isn't really in my mind defeasible.