Yes, Yevgeny Yevtushenko did protest the Soviet invasion of Czechoslovakia (JRL 7257), but to maintain his good standing with the Soviet authorities and continue his freedom to travel abroad, he also protested the American war in Vietnam.
I was duty officer at our Moscow embassy one Saturday afternoon in 1968 when I received a call from the Marine guard on the eight floor that a Russian was there who wanted to talk to an embassy officer. When I arrived at the marine desk, Yevtushenko was seated in the waiting room we had there awaiting my arrival. He appeared to be somewhat "under the influence," but he delivered his Vietnam protest to me in a firm voice. I heard him out and chatted with him for a few minutes before he departed.
Having made his amends with the authorities, Yevtushenko was able to resume his foreign travels, including visits to the United States. On one visit to Washington during the detente years, he was received by Richard Nixon at the White House and presented with a pair of presidential cuff links. For many Soviet intelligenty in those years, freedom came with a price. Some paid the price, others refused. Who are we to judge them now?