1. They were talking about newspapers. When Markle kept talking about "protection" and "support" in the interview, she was mostly referring to protection and support from negative headlines. She is very sensitive to negative press, as evidenced by her lawsuits & formal complaints against those in the press who are critical of her.
2. The only headline from a British paper that imo can be construed as racist was "Straight Outta Compton" when she & Harry were dating. That was insensitive and bordering on racist imo. That was before Harry sent the message to the press asking them to back off while they were dating (which they did, btw). There has been no other race-tinged coverage in the mainstream British press, however. Many of the headlines that Oprah showed during the interview were actually from American & Australian tabloids, NOT British tabloids (which are more respectable than American tabloids- the British tabloids are kind of like People magazine in terms of editorial quality- nothing like National Enquirer). One British headline in her montage was clipped from "'Meghan's seed will taint our Royal Family': UKIP chief's glamour model lover, 25, is suspended from the party over racist texts" to "Meghan's seed will taint our Royal Family". You see the difference? The newspaper had been reporting on a racist politician's comment & the response, and Oprah shortened it to appear as if the newspaper was stating that racist text as a headline. There was a talk radio personality who posted a social media picture of their baby as a chimp, and he, too, got cancelled over that. That was widely condemned and was never presented by the mainstream media. So just like in the U.S., the U.K. has individual racist jerks, but that wasn't the mainstream media or general public being racist against her.
3. The comparisons between her & Kate's press were taken out of context. Kate got plenty of harsh press during the long period when she was William's girlfriend (if you watch W & K's engagement interview, you'll notice that the interviewer even mentions it). She was nicknamed "Waity Katy" and criticized for not having a real career and basically just waiting for William to propose, and the press also criticized her as being a social climber, because she was middle class & dating a royal. In addition, if you go back a few decades and look at Diana & Fergie's press, you'll see some really horrific headlines. Upon H & M's engagement, Meghan got ecstatic press coverage. The coverage only began to tilt slightly negative after the kerfuffle with her father right before the wedding, and then later on it became much more critical once the couple began lecturing the British public on how to behave, while not following their own advice (ex: telling people to reduce their carbon footprint, while H & M used private jets multiple times in a week.)
The bottom line with their differing press coverage in the last few years is that they have behaved differently, so they've received different coverage. Kate is very careful about how she dresses and acts, and typically strives to follow royal protocol. Her focus is on supporting her husband, family and the monarchy. She has also maintained close, positive relationships with her family of origin and pre-royal friends. Meghan disregarded a lot of royal protocol during her short stint in the royal family, and it hurt her image: that protocol is actually there to protect the individual royals as much as it is to further the aims of the monarchy. She has cut off most of her family of origin, and many of her pre-royal friends, while inviting celebrities who she had only met once or twice to sit front and center at her wedding. Her focus is on self-fulfillment and making social change, and that isn't how the British public or press expect their royals to act. Hence, bad media coverage.
The British tabloid press is pretty straight up, and is going to call it like they see it. They aren't going to say, one positive story for Kate, so now we have to do a positive story for Meghan. They base their stories on how the royals actually behave.