This might be James Kahns "World enough and Time" (which is 80s fantasy and has a cat/human hybrid). From an Amazon review:
Along the way, Joshua and Beauty make new allies and defeat many
enemies. Among the former are Isis (part teenage girl, part black
cat), Jasmine (a centuries-old Neuroman, essentially a robot driven
by a human brain), Lon (a magnanimous and stately Vampire), and
Sum-thin (another Neuroman with a taste for philosophy and opium).
Among the latter are Jarl (a huge, talking bear king),
Poseidon-worshipping religious fanatics, more Accidents, a genetically
engineered dragon, some evil scientist Neuromans, and - of course -
the three original villains who had kidnapped Rose, Dicey, and Ollie.
Of these, Isis, Jarl, and all of the Vampire characters are sharply
defined and interesting.
While this is the first part in a a trilogy ("New World Trilogy") you probably want to skip parts two and three ("Time's Dark Laughter" and "Timefall") which are just as clumsily written but miss the naive charme of the first installment.
Here is another fun review (don't read if you want to retain fond memories of the book) from a reader who wasn't particularly thrilled, either:
World Enough, And Time (1980) is the story of a post-Apocalyptic
fantasy world, in which genetically-modified monsters threaten to wipe
out the remaining population of humans.
Having chapter after chapter of lengthy, pseudo-scientific
rationalization doesn't help me suspend disbelief, it merely bludgeons
to death any lingering excitement I may have had.
As the book limped to its action-packed, yet ultimately meaningless,
conclusion, I was stunned to find an ultimate reveal of... nothing.
The big bad fizzled, the relationships built on the journey dissipated
(there was a lot of shagging about for a pair of married men), and
everything culminated in a lot of standing about and avoiding one
another's gazes. Had I read this book backwards, it would've
essentially been exactly the same story. I have no doubt that there's
meaning in this - every leaf of every tree in World Enough, And Time
is packed with meaning - but I have absolutely no desire to seek it
If there's one positive about this book it is that, although Kahn
deluged the reader with world-building and philosophy, he spared us
any poetry. I appreciate the self-restraint.