There were always some people who had yellow during white periods and white during yellow periods, but:
Pre 1910: yellow (or rose) gold. The diamonds themselves were set in silver, or at the very end of the period, platinum, often with a gold shank or back. White gold had not yet been invented.
19teens: Platinum became popular. White gold was invented around WWI. Filigree styles in white metals were popular.
1920s: White metals and filigree styles continued popular. Geometric, deco styles came in, often with sapphire accents.
1930s: Depression. Jewelry became less elaborate. White metals still popular.
1940s: WWII brought a platinum shortage. Palladium was sometimes--briefly--used as a substitute. Yellow gold began coming back. After WWII, the retro style came in. Rose gold was popular briefly at the end of the decade.
1950-60s: White metals came back, especially for diamonds, but yellow gold remained popular as well.
1970s-1980s: Yellow gold was in. White was out.
Mid-1990s-mid 2000s: Yellow gold was out, white metals were in.
Mid-2000s-now: Rose gold is in. Yellow gold is coming back. White metals are still popular, especially for bridal jewelry.
To sum: Fashions come and go. Wear what you find beautiful.
I got engaged 1979. No one I knew (my age) had white gold. My grandmother had platinum (1926) as did my mother and MIL (1954). My step mother got platinum also (1965).