Some may quote Matt 8 to excuse themselves from caring for their parents...
Matt 8:21, 22 - Then another of the disciples said to him: "Lord, permit me first to go and bury my father." Jesus said to him: "Keep following me, and let the dead bury their dead."
HOWEVER...
One explanation of this account is that the man was lying and giving excuses. If the man's father had indeed died at that time, he would have been with his family instead of being with Jesus! The man's father had likely died much earlier and was already buried! Jesus could well have been exposing the man's hypocrisy when he said "Let the dead bury their dead," indicating that he KNEW the man's father was already dead & buried!
Now lets see what example Jesus set in the following account:
Mark 1:30, 31 - Now Simon's mother-in-law was lying down sick with a fever, and they at once told him about her. Going to her, he took her by the hand and raised her up.
Notice that Jesus here set a fine example on the importance of caring for family members. The person involved was not Peter's OWN mother, but his mother-in-law. Yet, her needs were cared for
Likewise, IF modern day Christians DO NOT care for the needs of their aging parents or in-laws, then the scripture in 1 Tim 5:8 would apply fully to them