Prince Karl-Theodor, Duke in Bavaria (9 August 1839 – 30 November 1909), was a member of the House of Wittelsbach and a professional oculist. He was the favorite brother of the Empress Elisabeth of Austria, and father of Queen Elisabeth of the Belgians.
In 1877 Karl-Theodor began practicing medicine in Mentone on the Côte d'Azur, often assisted by his wife Maria Josepha. In 1880 he opened an eye-clinic in his castle at Tegernsee. In 1895 he founded the Augenklinik Herzog Carl Theodor (English: Duke Charles Theodore Eye Clinic) in Munich; the clinic in the Nymphenburger Strasse remains one of the most respected eye clinics in Bavaria to the present day. Between 1895 and 1909 Carl Theodor personally carried out more than 5,000 cataract operations as well as treating countless other eye disorders.
He married twice. First to an Infanta of Portugal and second to a Princess of Saxony.
Despite being a Prince of Bavaria and a medical Doctor he kept his titles.
What Princess Elisabeth are you referring to? I'm afraid the only one that comes to mind is the one in the Belgian royal family. Anyway, you pose an interesting question. The short answer is yes and no. It depends on what type of work. If it is a 9-5 job, my guess is there would be some resentment if fellow employees thought the royal was getting preferential treatment. The answer to your question also would depend on how much the royal was expecting due deference to his/her royal rank.
I remember the publicity regarding Prince Andrew while serving in the Navy. You may recall the story when he first went aboard ship. Introductions were made and Andrew was presented to a superior officer. He told the officer, "You may call me Andrew." To which the officer replied, "And you may call me "Sir."
Back to your question, I would say no to your question because most of the jobs I hear royals taking on are those that appear to be more flexible. The royal is either self-employed as Prince Edward was with his Ardent Production Company or something along the lines of what Princess Eugenie does. I gather she works at an Art Gallery, but appears to be almost self-employed as she oversees events, etc. Also, it seems to be more part-time as she is seen in the press as either traveling or attending evening functions. I doubt she is running into much resentment from fellow workers.
But, alas, the information I have is these jobs are mostly short-term and have ended on a sour note as Edward's was with his attempt to carve out a meaningful career. As I recall, he was upset because he claimed of bias in the media. He was accused of trading on his royal status and most of his work was panned. I myself thought his documentary on his uncle the Duke of Windsor was very good. And were he not a Royal, he very well could have made a success of it.
Permit me to digress for a moment onto another topic.
Royal Houses today are well aware that Republicanism is always nipping at their heels. Prince Nikolai, in particular, is involved in a highly competitive commercial enterprise. Publicity surrounding him makes use of the Prince of Denmark title. Queen Margrethe may be attuned to public reaction to a Prince helping sell clothing that her average subject cannot afford.
I don't know why Nikolai doesn't just use his first name as many high-profile models do.(Think Iman).He obviously has real talent. I think Nikolai could make it without the Prince title.
Princess Elisabeth was able to have a career while being a princess. Did she have trouble in that regard? Did her co-workers resent her status?