Actually, I always wondered what the situation was in Nancy Astor's day. Did she get her citizenship removed as soon as she married Waldorf
Probably, yes. They married in 1906. Waldorf Astor was also born in the US, but is reported to have become a naturalised British citizen. Dual nationality was not allowed at the time.
The 1907 Expatriation Act stated that any American woman who married a foreign man lost her US citizenship. The same did NOT apply to American men who married foreign women.
The Cable Act of 1922 altered that slightly. An American woman was allowed to marry a foreign man and not lose her US citizenship, provided she remained in the US. If she lived outside the US for 2 years, then she lost US citizenship.
"Did the US tax them?"
Taxation of foreign income of US citizens who were non-resident began in 1864; was repealed in 1872; made law again in 1894; declared unconstitutional in 1895 by the Supreme Court; and made law again in the 1913 to 1916 income tax reform. It has only been challenged once since, in 1924 when the Supreme Court ruled it constitutional.
All this is from the interwebby, so accuracy is not guaranteed!