Cruz represents his constituency and I think he's said plenty of things that reflect that, like a week after Charlottesville, he came out and condemned white supremacy. There is nothing wrong with gauging the sentiment of your constituency and then, making a comment.
Kicking someone off of committees as King has been, has to be somewhat of a death penalty for his seat as a representative. Is this for a temporary period or forever?
Though these are or appear to be left-wing sources, he was already getting into hot water (even more than before), last October:
Oct 25, 2018
Rep. Steve King Goes Full White Nationalist In Interview With Austrian Site
https://www.huffingtonpost.com/entry/iowa-rep-steve-king-austria-white-nationalist_us_5bca4851e4b0a8f17eec6001
And look, this is from 2016!
December 23, 2016
Steve King Met with Leaders of Trump-Friendly Austrian Party with Nazi Roots
http://iowainformer.com/politics/2016/12/steve-king-trump-nazi-freedom-party/
(granted, Nazi roots is a bit dramatic, but it does mean, they were around back in the day, a topic to research by itself)
This is not some brand new thing, I think an investigation should have been done first but King should have known, he had no room for error, he is either incredibly naive or does reflect far out opinions.