Golden Rule, 'do unto others', be the change you want to see in the world - many ways of saying/looking at the same stance. If someone asks for help and I'm able without causing myself issue, I feel compelled to do what I can. Within reason.
I feel like this is where most people diverge. What's within reason? Isn't true kindness, rather selflessness, LOVE in a fundamental way defined by giving at your own cost or peril? The question is how much you are willing to give. A Buddhist monk gives everything, your average Joe donates 5 euro a month to charity - How much is within reason?  
When kindness is seen as weakness it screws everything. There are so many 'good' people who got burned too many times leading them to become jaded and bitter, refusing to lend even the most basic hand to someone in dire need.
True and part of me wonders whether their kindness was truly kind to begin with. 
I am not judging people for being flawed, but we are exploring true selflessness here
Free market capitalism has instilled this idea that if something doesn't profit you it's not worth the time and effort. This has led the sense of community, in it's truest form, to deteriorate leading to incredible isolation even in large cities. The resulting alienation fuels ever increasing numbers of mental illness and unprovoked violence.  
It benefits everyone if we make an effort to engage others with kindness,
Indeed, it's the same old story.. There is something to be said for the power of rebound - People tend to relish in contrast and it feels good to rebel against a hollow society through kindness, sometimes even more so than in a society which is already kind. Perhaps some deeper part of us is actively guiding us toward these conflicting tendencies
unless there's good reason not to, of course.
Interesting how often you feel the need to make this caveat. You're setting some strong boundaries :D