LAguy is absolutely right. Yichus in middos is way more important than yichus as we define it. I knew what kind of man my husband is, and when I met his parents for the first time, I immediately knew WHY he was that kind of man. he grew up in a non-frum home that was filled with more chessed than you can imagine. His parents took care of both sets of grandparents in his home(first the maternal grandparents, until they died, and then his paternal grandmother until she passed), his mom’s sister who was prematurely widowed and left with two small children, whom my mother-in-law helped to raise while her sister went out to work, and then when my dear MIL had a devastating stroke at age 42, my wonderful FIL took care of her until the day she died, for the next 35 years. he did so, not only without a word of complaint, but with letting her feel like she was still the akeres habayis. No easy feat with someone who was totally bedridden and helpless. Everything was done with love and true chesed, and fortunately that is what my children remember, more than the fact that their grandma was bedridden and blind.
Now, every BT is not filled with chesed, just as every FFB is not. There are nice and friendly people and there are nasty people in every strata of life. But we do have an achrayus to be welcoming to BT, to give them chizuk, and to make them feel they are truly part of the klal. That does not necessarily result in shidduchim with them, but maybe it is our achrayus to try and help them FIND the right shidduch…