It happened to my kinship as well on Riddermark some time ago.
You have those people on the server, and you live and learn. What we decided to do is to leave the kinship chest open for everyone EXCEPT recruits, and all new members are recruit for a week. There are always exceptions, such as good friends we know, etc, but if we don't know someone they will be recruit for a week to get to know them.
Second, we no longer keep valuables in the chests. We store easy to get crafting items such as hides, cosmetics, perhaps some level 100 dropped items that are very common, 3d age weapons for deconstructing, that kind of stuff. The more valuable things are kept with officers, either in their own houses (and officers have access to eachother's chests in some cases) or on an alt "mule".
Another thing I have considered is an "officer's house". This would be just a free account, a character leveled to 15, given money to buy a deluxe house, and enough to buy storage till it hits the mithril coin level, and buy that house in the same neighborhood as the kinship house, as close as possible. Then, the owner of said house will give access to every officer possible. Officers can now store valuables in that house, while still leaving the actual kinship house a free-for-all open chest.
Moved from Riddermark to Arkenstone on 9/29/2015!
Disclaimer: The definition of "Soon™" is based solely on Turbine's interpretation of the word, and all similarities with dictionary definitions of the word "Soon™" are purely coincidental and should not be interpreted as a time frame that will come to pass within a reasonable amount of time.