it was common for British nobles taking

And according to Lauren A Siegel, a tourism and events lecturer at the University of Greenwich in London, as recently as the 18th and 19th Centuries, it was common for British nobles taking the Grand Tour of Europe to belittle and disregard the people and places they were visiting.

Source: Is this the summer of bad tourists? by Larry Bleiberg


Are they the same in meaning?
1. ... British nobles taking the Grand Tour...
2. ... British nobles to take the Grand Tour...

#2 is incorrect.

Ah! ...it was common for British nobles (who were) taking the Grand Tour of Europe to belittle... Am I correct?

Yes. You had parsed the sentence incorrectly. You have it right now.