Creating a caring culture?

How do you create a caring culture?  How so you ensure that caring culture is caring towards all equally?  In Acts 6 we see one element of the early churches caring culture in its provision of food to widows, but we also see how imperfect this care is as some grumble that they are being overlooked.  The answer is a practical one as the fair distribution of care is sorted out by appointing a team to oversee this care of all.

Sometimes when we preach on the need for loving one another deeply or constantly we assume that the job is done, automatically people we start to love one another deeply.  We may even see cases of that happening in the church as we look.  But we need to ask; how even is it?  Are there people who are not being cared for?  Are there people who are missing out?

Primarily care in church happens as people invest in church and the relationships people find there.  So you are cared for as you go along on Sunday as the bible is taught and as people encourage you.  You are cared for in your small group or gospel group or whatever you call it as you go along and invest.  You are cared for in the toddler group or men's or women's bible study.  It doesn't happen automatically but as you access God's word to you and invest in others you grow and develop caring relationships.

But who do those groups leave out?  And how do we care for those who are outside of those groups in which care is easier?  How do we best care for those who opt out of those sorts of groups?

I'd love to know how others do this, what they've found works and what doesn't?