Although Kate had her own bumps on the road, I don't think her situation is at all comparable to Meghan's. Kate fit in surprisingly well, much better actually than Diana, who was a bit of a disaster despite her "superior" ancestry (I mean, compared to Kate's middle-class background).
Meghan is an outsider in ways that Kate or Camilla for that matter are not, so it's always going to be tougher for her. She could learn, however, from her sister-in-law and stepmother-in-law on how to keep a lower profile and be more discreet. A situation like the baby shower was perfectly avoidable.
I don't think it's possible for Meghan to keep a low profile, part of it is just based on who she is mixed-race, American. In addition Meghan became a full-time working royal the minute she and Harry got married and was expected to 'hit the ground running'; her first engagement was 3 days after her marriage. Kate had the luxury of easing into the role. Meghan has also already been assigned a couple of overseas tours the most recent one in Morocco attracted over 100 press/media (and from the reports I have seen almost half weren't British). She and Harry are strong relatable Ambassadors for the UK right now and it would be wise of the BRF and the UK to take advantage of that.