Yes outdated mods and custom content can make your break your game.
If you haven't already, move your mods folder to the desktop, clear your game cache and delete the localthumbcache.package from the Sims 4 folder to help with troubleshooting. Try playing the game again to test. If it loads okay, it may be that some of the mods/cc have become outdated.
How to Fix Problems with Mods/CC
http://www.carls-sims-4-guide.com/forum/index.php?topic=25031.msg426156#msg426156Mods and custom content can become outdated with most new game patches. If the game works when the Mods folder is removed, then one or more of the mods and/or custom content have become outdated and will need to be removed or replaced.
EA/Maxis aren't responsible for broken mods/cc. It's up to the creators to fix.
Testing by disabling mods in the Options Menu, isn't enough of a test to be able to tell if it is a mods problem, a cc problem or a vanilla game problem.