No. Few Catholics that I know of define themselves as non-EO. On the other hand, I know of many EO (often ex-Catholics or ex-Protestants) in person and online who at least partially define themselves by their antipathy to Catholicism.
It's not surprising. Look at Canada for an analogy. The USA is so much bigger and more visible and consequential (for better or worse), and many Canadians can't help but have some antipathy and define themselves as definitely-not American. It's human nature. Just as Canadians always raise the alarm about becoming Americanized, for centuries now the EO have been arguing over becoming Latinized. Some of these arguments have been catalysts for EO schisms which still persist.
I have seen plenty of this in EO circles, especially among converts. Since the Catholic Church is so much bigger than the EO churches, obviously the ex-Catholic EO are going to be more visible. The global Catholic Church, being the much bigger and far more visible half of the formerly undivided Church, and having millions of Eastern Catholics under it, understandably causes some antipathy in the little-regarded EO churches, most of whose members are concentrated in Eastern Europe.
I can still vividly recall the ugly reactions (among both laity and hierarchy) to John Paul II's visit to Greece a few years ago. Can you imagine the Patriarchs of Moscow or Constantinople getting a reaction like that anywhere in the Catholic world?
Witness also the cottage industry of EO books attacking Catholic beliefs and the very heated arguments among EO leaders and theologians over ecumenism. It's a huge controversy.