Modern Warfare causing consoles to brick hasn't been proven, but it's understandable why people would say so. "Bricking" consoles is the theory that games cause a console to break or not work and become a useless brick in their living room.
There have been many errors with the game, but none more than any other shooter at launch. It can really pertain to your luck and internet connection.
Modern Warfare Bricking Consoles: Does Modern Warfare 'Brick Consoles?'
Call of Duty has recently started their first Battle Pass season and released a lot of updates. Those updates have been causing errors in some players systems. But overall, they should not render your console obsolete.
One of the main ones is Error Code 262146. First, read the message given, "You have been disconnected from the Call of Duty: Modern Warfare servers. Please try again or visit https://support.activision.com/mwstatus for updates. Error Code: 262146."
Head to the support website will simply show you dozens of posts of similar problems and Activision with no solutions. Sadly, it usually takes time for this problem to be fixed. You can give it a few hours before logging on again, while most have simply stated the problem was gone the following day.
Players on the Modern Warfare subreddit have tried simple fixes with some success. Such as resetting your modem or router, logging in and out of your profile on you specific device, or in some drastic cases, re-installing the game. I would avoid that last one unless the problem has persisted over many days.