First off, note that the idiom is "I brake for…", not "I break for…".
I imagine it's a reference to cautionary signs placed on the back of certain vehicles. For example, in the US, it's common to see signs like this on school buses or service vehicles:
This vehicle stops at all railroad crossings
This vehicle stops at all red lights
This vehicle makes frequent stops
So a cautionary sign like
I brake for squirrels
Would be superficially similar—warning others that the vehicle may make a sudden stop if a squirrel happens to cross the road—although it's primary goal is to alert others to the driver's special love of squirrels.
This was later extended to "I brake for X" where X is anything the driver feels special affection for or attraction to even if there is little or no possibility of encountering it while driving (e.g. "I brake for smurfs").
The cautionary sense of the idiom may still apply, for example in the bumper sticker "I brake for tailgaters", which clearly does not indicate any kind of affection.