Russian cosmonauts cannot fly on Boeing Starliner aircraft, regardless of whether an agreement is reached between the State Corporation Roscosmos and NASA to cross-flights the International Space Station. RBC reports on this using the words of Dmitry Rogozin (head of Roscosmos)
The only way that American and European astronauts could fly was on Russian ships. Cross-flights were offered by the American side to ensure they do not lose their flying abilities. Also, it is known that the possibility of a Russian Cosmonaut flying on an American Ship was discussed last year (it was believed that Russian Anna Kikina would fly into space on SpaceX Crew Dragon). The situation has changed since the escalation of the Ukrainian situation. Rogozin said that it is too soon to make a decision about cross-flights to NASA. According to Rogozin, it is impossible for Russian cosmonauts to fly on American vessels due the insufficient level security.
“Big troubles happen on Musk’s ship, including the failure of the sewer system <…>, this is a life support system, this is not a joke, if these failures continue, it’s difficult for us to make a decision on a cross flight for now, send our girl to their ship”Dmitry Rogozin agreed. Dmitry Rogozin also believes it impossible that Russian cosmonauts could fly on the Boeing Starliner. The first flight was an accident and the second is still not completed. “Now they will try to launch it, but we definitely won’t put any of our astronauts on it. Their lives are too important for us to risk.”Roskosmos’ chief stated this.