Do we know if it was just one text message at 5 a.m. or if it occured repeatedly? If it did occur repeatedly, did Meghan know if the staff had their cell phone by their bedside (and would be woken by the message?) If she knew and sent those texts anyway then I don't think it has anything to do with cultural difference. I'd consider that rude and respectless.
Even if she didn't know, I think it's a sign of respect if one refrains from sending the text message if they don't know if they'll wake the other person and then ask, regardless of what the relationship to that person is.
I'm also not quite sure why the discussion centers around the text messages when there seem to be have been other issues as well. I'm not under the impression that the bullying is only because of text messages.

If memory serves, Meghan also did not have a stylist. I don't think there's anything wrong with that but I wouldn't be surprised if that were an issue of contention when you're a member of the BRF.
One of the nice things with many of the European royals is that they
seem to be friendly with one another. That's another support system that UK royals don't appear to have.
Speaking of friendliness among the European Royals: one difference between Germany and the US is how quickly you make acquatainces. I had an easy time making friends in school in the US (where I went to school for only a year) while it was much harder for me in my native Germany. The same was true for my time in France, much harder. So, I find it entirely possible that the people Meghan met in the UK were more reserved and that that might have led to misunderstandings.
Generally, I wish they could all sit down together and talk things through. Things seemed to be going so well at the beginning and then it took a 180 turn and I find it especially sad because William and Harry were so close before. After what they had gone through they would have deserved to remain close throughout adulthood. I hope they'll be able to sort things out over time!
I'll say it just this once more: I think it was a mistake for the BRF to announce this investigation. I don't think they are going to win this war. As Meghan's co-star points out in his thread ... They're taking on a woman who is the wife of a current heir (however far down) and mother to two other heirs.
I'm not sure what Meghan's co-star is trying to say or imply. If the BRF did announce the investigation then it would be sanctioned by the Queen, wouldn't it? And I think she easily wins a war based on status within the family. Likewise, if William leaked the investigation as I think was implied.
Harry and his brother thought it was OK to go to a "natives and colonials" fancy dress party.
(and yes I know they apologized later on)
How Nazi gear, a popular society choice, put Harry in the doghouse.
www.theguardian.com
From what I've seen and heard, I'd say many Brits have a rather lax view on things like that. That doesn't make it right and I think it needs to change! I'm just saying that this is likely the way they were raised. And Harry still fell in love with and married Meghan, so I don't think it necessarily says anythng about how racist they are. But I do believe that an attitude like that (thinking attending such a party is ok) makes one less sensitive to and/or less aware of the issues of (systemic) racism and it's also possible that it causes involuntary (I'm not sure if this is exactly the right word) racism.