Not treason at all. You're not swearing allegiance to the Monarch at the expense of the States. The one major thing we have is that it is illegal to create a title a title of nobility. You can't even accept one without permission if you're in government.
"Article 1 section nine of the US constitution:
The question of bowing and curtseying has always been a vexed one where citizens of the United States are concerned.
I can remember that there was press interest on both sides of the Atlantic when President Reagan and his wife Nancy made their State Visit - the 'will they / won't they' bow/curtsey' question was raised for some weeks. IIRC, Nancy executed a subtle bow of the head when meeting the Queen. President Reagan was able to sidestep the issue very neatly because, as he was over 6ft tall, and Her Majesty around 5ft 4in, he
naturallyhad to incline his head when meeting her.
End of problem; if it ever really arose in the first place. American citizens traditionally show respect by addressing their Head of State as 'Mr President'; Subjects of Her Majesty generally - or used to - show respect by executing a bow or a curtsey. There is no difference in reality; as we say in England, it is just a case of your tongue doing the work [United States] or your neck/knee [UK].
Historically, there has never been a difficult in American Citizens curtseying. When Joseph P Kennedy [father of JFK] was United States Ambassador to the United Kingdom, some of his daughters were actually presented at Court, which required them to perform formal court curtseys. Which they did and without any complaint. [This is really a story for another thread, but Joseph Kennedy outraged many prominent London-based American Citizens by
refusing their requests to allow
their own wives and daughters to be presented. [It was one of the roles of an Ambassador's wife to present 'suitably qualified' ladies from her country at court; one of my great aunts had a great American friend, but there was nothing that could be done to secure the presentation of either this lady or her daughters; it was down to the Ambassador and if he was not willing for his wife to present somebody, then there was nothing that could be done].
Hope this is of interest vis-a-vis any 'difficulties' which might be seen in respect of Dave. For well over 100 years, there have been prominent American citizens who have married into the British aristocracy with no difficulty whatsover when these citizens have then become closely involved with royalty. I reckon that he will fit in easily into royal society. Whist it is seems to be the case that neither Beatrice or Eugenie will undertake royal duties, they will always remain members of the Royal family and in my humble opinion, the girls will still be important members of the Royal Family. Take the case of Peter Phillips; he has no title and has a career that is totally independent of the Royal family. Yet he still attends family occasions - visits to Windsor and Sandringham etc. And when he does so, the staff are instructed to call him 'Sir', as is the case with other 'working' 'titled' royals. And so, for this reason, I am fairly sure that Beatrice and Eugenie [and their eventual spouses] will still be treated in a similar way to their working/titled royal relatives.
Hope some of this is of interest
Alex