World number 15 Kasatkina has not returned to Russia in over two and a half years and was living in Dubai when her change of nationality was announced.
“With everything going on in my previous country, I didn’t have much choice [to switch allegiance],” the 28-year-old told reporters last month.
“For me, being openly gay, if I want to be myself, I have to make this step, and I did it.”
Kostyuk, 22, was booed off court at the 2023 French Open for not shaking hands with Aryna Sabalenka of Belarus and said afterwards people should be “embarrassed” by their reaction.
“Some say sport should stay out of politics, but this isn’t politics – it’s about humanity,” Kostyuk wrote on Friday.
“When your country is under attack by an aggressor, silence feels like complicity.
“As an athlete, I believe in fair play and respect – but those principles mean little if they don’t extend beyond the court.”
Earlier in 2023 Kostyuk also refused to shake the hand of her Russian opponent, Vavara Gracheva, after winning a first WTA title in Texas.
Gracheva has since become a French national.
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