How to prevent random console output from breaking the terminal?

No:

• there is no standard way to "disable it", and
• the details of breakage are actually terminal-specific, but
• there are some commonly-implemented features for which you can get misbehavior.

For commonly-implemented features, look to the VT100-style alternate character set, which is activated by ^N and ^O (enable/disable). That may be suppressed in some terminals when using UTF-8 mode, but the same terminals have ample opportunity for trashing your screen (talking about GNU screen, Linux console, PuTTY here) with the escape sequences they do recognize.

Some of the other escape sequences for instance rely upon responses from the terminal to a query (escape sequence) by the host. If the host does not expect it, the result is trash on the screen.

In other cases (seen for instance in network devices with hardcoded escape sequences for the Linux console), other terminals will see that as miscoded, and seem to freeze.

So... you could focus on just one terminal, prune out whatever looks like a nuisance (as for instance, some suggest removing the ability to use the mouse for positioning in editors), and you might get something which has no apparent holes. But that's only one terminal.