As a matter of pure sound, "leftuge" is a smart portmanteau - it works in speech the way something like "rightfugee" would not.
Whether it works as a realistic description is much more arguable.
The term is relatively new - just starting gain traction in late 2019 and early 2020, though the idea behind goes back many years. The concept is that, as some states - California would be the prime example - have become bluer and ideologically more left-situated, people have departed them for redder and right-situated states.
This relates to the idea of the "big sort," which got its big push with the 2004 publication of a book of that name by Bill Bishop. (The subtitle is, "Why the Clustering of Like-Minded American is Tearing Us Apart.") Bishop's thesis was that, increasingly, Americans have started to move to where they find more people like themselves. In the past, the politics of a place has tended to be a by-product of whoever came there for other reasons. More recently, it has become a reason to move.
Bishop's argument has been attacked at times and it has limitations, but there's clearly a good deal of evidence for it to some extent at least. Anecdotally, many of us probably know of people who moved to "red" to "blue" or the other way around with the idea of residing in a more agreeable location, maybe with more people in residence who agree with oneself. Statistically, we know that states, congressional districts and other jurisdictions increasingly have become brighter red or blue, with ever fewer purple (such as genuinely partisan-competitive congressional or legislative districts) areas remaining.
The sort has been a two-way street. Not so very long ago, California tilted red, but as the population mix and issues changed, it overall turned deep blue. The many red-tinged people remaining became less comfortable with that, and some of them moved out. But the phenomenon is not new. Even back in the 60s, even as Ronald Reagan was elected governor there, conservatives moved out of California in hopes of finding a promised land elsewhere. (I knew one of them, a Goldwater supporter from Orange County who moved to northern Idaho and was one of the drivers of political change to the right there.) But the reverse is true too; many rural areas have become emptied out of blue-leaning people seeking more agreeable places (often in metro areas across many states). Colorado's recent arrivals have been a key reason that state has moved into the blue column.
California's relatively recent wave of departures, thought likely to be enough to cost the state a congressional district after 2020, may have some ideological component. But other factors likely are at play too, notably the state's extraordinarily high residential housing prices (which in turn resulted mostly from demand). The Trulia web site said that the top recipients of these departures are sunbelt metro areas like Houston, Atlanta and Phoenix. On one hand, these places are located in what have been red states.
A Washington Post article noted that "Conservatives have even coined a new word for these people: 'leftugees.' As the moniker implies, Republicans are inclined to declare ideological victory, given that so many people seem to be voting with their feet against Blue America’s policies."
That's one piece of the picture and does apply to some people. But it's not the whole story: These arrivals also are going to metro areas which have become largely blue, and which are contributing to the rapid purpling of their respective states.
People move, and for lots of reasons.