Can't add any pets from the gallery

@xXxCleverNamexXx 

Cleaning mods folder is not enough sometimes. There are mods which create files in your saves folder also.
But in this case, I suspect some of your CC caused it.
after adding Dogs and cats, many of your CC's were no longer compatible with the game. If you enabled the mods option in the game and enabled the game, the game files could be damaged. Although you removed the CC afterward, that damage has not been repaired
How to fix it:

First, check if there are new versions of mods and CC that you use

Step 1. Rename The Sims4 folder to "The Sims4 old"
Step 2. Fix the game in Origin
Origin/Library - right click on TS4 - option "Repair game"
You have to wait until Origin will fix all packs, not only the base game.
Step 3. Turn on the game - a new game folder will be created and you will have two - one old, one new
Step 4. Check if you still have this problem in the newly created game folder
If the problem disappeared
Step 5. Delete in the new game folder following folders:
"saves" and Tray.
Step 6. Go to "The Sims 4 old" folder and copy - your "saves " folder.
Step. 7, Paste this folder in a newly created game folder.
Step 8. Do the same with Tray folder and TrayDeleteItems file
Step 9. Copy and paste your mods and CC from old mods folder to a new one. First copy the scripts mods every time checking if the game is working properly. If you have a lot of CC try 50/50 method
Step. 10. If all is OK - delete The Sims4 old folder. Now you will have only one game folder working properly.

I don't work for EA.