More great suggestions, thanks!
I would tend to exclude some games for the reasons I will specify, while for others I would need some more data.

Games definitely included in the list:
Rusty Lake Hotel - all the main characters are anthropomorphic animals.
The Aquatic Adventure of the Last Human - all enemies in the game are animals and are constantly part of the game experience.
Abzu - fish everywhere (in the game it's specified that we are in the prehistoric Earth?)
Anna's Quest - It seems that there are many animals in the game
Little Big Adventure - Also here there is the presence of many anthropomorphic animals. In the sequel they are still there? Is it ever specified what the world of LBA is? Is it Earth, a fantasy world or something else?

Excluded games:
Blasphemous
Reigns
The Count Lucanor
Downwell
Stasis
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For these games the presence of animals is more of a cameo, so I would exclude them or I would have to add every single game where dogs, cats, horses or cows appear in the background, and there would definitely be hundreds.

Slain - I remember the level with the wolf, but again I'd lean towards a fleeting appearance rather than an important character in the game.

Rain World - This is a great game, but I don't remember if it's ever specified if it's the Earth of the future or an alien world. In the second case I would exclude the game from the list to put it in a future one about alien creatures.
A real bear that can be added to the party makes Baldur's Gate 2: Enhanced Edition a great candidate, thanks for that clarification! I wonder if Wilson also exists in the original version of the game.

I am very sure that Wilson was an Enhanced Edition edition, and was not in the original game.

LBA: it's set on an imaginary planet and the humanoid animals are still there in the sequel!
A curious fact about Reigns: you can date the pigeon for a Boyfriend achievement, and it's of course blinking the eye to Hatoful Boyfriend.
In the recently added When the Past Was Around one of the two main characters is a humanoid owl.
https://www.gog.com/game/when_the_past_was_around

That's pretty much what I imagined. Thanks!

GEX
MDK 2

Both great games imo.

Now I remember Ys 8. Is not listed maybe because is a bit gray in terms of animals presence for this post? You fight tons of animals, prehistorik animals and dinosaurs. Some of them even help you on your quest (but aren't part of the party)

It's hard to mention another game on GGO where animal presence is significant. There's plenty of animals in many games, like all the crows in the Last Door, but nothing to list here that I can't think of and is not in the list already. We don't even have Armello anymore!
Do GOG curators dislike animals? No Aviary Attorney, no Moss, nothing.
I think Inkulinati can do. All fighters are animals drawn in the style of the Middle Ages.
Biomutant is not out yet but announced on GOG.

I see that you have rejected Owlboy (!) so I'm not sure of whot you would think of Way of the Red and its birdman race.

Thea 1
https://www.gog.com/game/thea_the_awakening

Thea 2
https://www.gog.com/game/thea_2_the_shattering

Not sure if they would count. (Alien world?) You can get animals as party members.
In Thea 2 you can (once you unlocked them) even chose a rat/wolf/snake/spider as your "chosen" (= main character) or just as a starting group member.

Timberborn has Beavers as protagonists (Alien world?). Not out yet.
https://www.gog.com/game/timberborn

Here is one that does seem to belong on your list as well Metamorphosis In it your character is a cockroach with lots of others around ... *yuck*

There is also Entomoroph - Plague of the Darkfall which I wasn't aware we got it here!

I should also like to suggest Staxel
and ... *thinks* ... My Time at Portia
and finally Stardew Valley

In Entomorph, according to the backstory, aren't at least some of the insect enemies actually humans transformed into insects?

Hey speaking of insects, in Bad Mojo Redux you control a cockroach and other characters are insects too.
Main character is originally a human I think, turned into a cockroach. But the other insects are "real" insects.

If I remember correctly the queen was turned into one. Whether this is also true for other inhabitants? I can't really say but it is very possible. What I do remember is that PC can turn into an insect or decide not to, which greatly limited options, versus ingesting poisons to morph and take different paths to save your own hide, and/or humankind as it was.

Add. Question: As I don't use the client, what I seem to have read is that there is no way to universally add tags so others don't have to. Maybe there is a way to do it once and share the fruits of your labor with others. My question is whether there is a .csv file stored locally containing a list of tags and games. In that case this could be uploaded and only games one doesn't own and tags one doesn't like would have to be deleted from that file when using it for one's own library. Would make the process much quicker for any upcoming effort to add further tags for different sets of games. The question is, is there such a file?

While the roster varies from game to game, the Age of Wonders series has both animals (as hostiles and potentially as units) and anthropomorphic animals as units and/or factions (whether as the result of wizardly meddling in 1-3, or genetic engineering in Planetfall - some of earth-origin so they aren't just 'aliens').

Ultima Underworld 2: Labyrinth of Worlds should be on the list alongside the others from the series. None playable, but various animal enemies and some animal NPCs appear.

Heretic Kingdoms: The Inqusition, and Shadows: Awakening are a two-part series with anthropomorphic wolves as both hostiles and NPCs, and one can be part of your 'party' in the latter.

Would the Hotline Miami games qualify for this category?

In the first game especially the protagonist dons various animal masks on his killing sprees that grant him with different abilities and some of the characters in the second game also wear such masks.

Thanks again to all, let's see what are the new additions:

Little Big Adventure 2
When the Past Was Around
Gex
MDK 2 - If anyone knows why the dog has 4 arms I am curious to know why XD
Inkulinati
Thea: The Awakening
Thea 2: The Shattering - Thea looks like it's set in an alternate fantasy-style Earth, so if animals play a substantial part I'd say they can be included.
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Metamorphosis
Entomorph: Plague of the Darkfall
Bad Mojo Redux - In addition to all the insectoid npc and enemies of these games, since I accept anthropomorphized animals I think that in any case it's right to accept "animalized" humans.
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Staxel
My Time At Portia
Stardew Valley - In these titles raising animals and taking care of them is actually a big part of the game so I'd consider them part of the list without issue.
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Age of Wonders
Age of Wonders 2: The Wizard's Throne
Age of Wonders 3
Ultima Underworld 2: Labyrinth of Worlds
Heretic Kingdoms: The Inquisition
Shadows: Heretic Kingdoms
Shadows: Awakening - Other fantasy titles that seem to fit easily into the rules. Is Planetfall set on Earth?

Biomutant - Looks like an Earth of the future, but could be an alien world, we'll see when the game comes out
Ys 8 - There seem to be plenty of monstrous creatures, but none really inspired by animals. I'm intrigued by the presence of dinosaurs, but I would need more detailed information.
Way of the Red - I don't know what to think of this game, it's not clear to me if the main character is an alien species or if everything takes place in a fantasy Earth. Owlboy is still in doubt as far as I'm concerned, I'll have to look into it further. XD
Hotline Miami - I was tempted to add them, but being simple masks I don't think they can make the list.

I hope I haven't forgotten anything, let me know if you have any other comments or objections!

Honestly I don't know, I only know that the tags are stored on the cloud by GOG because they remain visible from one computer to another with the same account. To know if there is also a file on the PC that keeps the information would need the help of someone more experienced. Also, there would remain the problem that you can't tag a game you don't own, so presumably a lot of games would be left out unless the first person to tag has an endless library.