I dont know how someone might consider 1 Ti 5:8 in respects to disobedience and denying the faith, but there is (in that) becoming worse then an infidel could play in but there is professing to know God and being abominable and disobedient and unto every good work reprobate Titus 1:16. Im not sure how the doctrines of each camp deal various scriptures though
If one does not provide (ie. serve) those whom they profess to love (especially immediate family) that one has obviously denied the faith which is established upon love. Such a person professing to be a Christian is worse than an infidel because of the hypocrisy involved and thus ought to be rebuked openly before the congregation. It is a very serious matter for sin service to be found in the church, not only for the dire state of the individual involved but for the effect it will have on those around them (ie. it draws others into sin).
Being disobedient unto every good work is simply an allusion to professed righteousness. A good example would be a Christian charity worker who is still engaged in all manner of vile sin in secret. Israel was serves us as an example of such in the words of Isaiah...
Isa 29:13 Wherefore the Lord said, Forasmuch as this people draw near me with their mouth, and with their lips do honour me, but have removed their heart far from me, and their fear toward me is taught by the precept of men:
A statement Jesus referred to in...
Mat 15:7
Ye hypocrites, well did Esaias prophesy of you, saying,
Mat 15:8
This people draweth nigh unto me with their mouth, and honoureth me with their lips; but their heart is far from me.
Mat 15:9
But in vain they do worship me, teaching for doctrines the commandments of men.
Mat 15:10 And he called the multitude, and said unto them,
Hear, and understand:
Mat 15:11
Not that which goeth into the mouth defileth a man; but that which cometh out of the mouth, this defileth a man.
Mat 15:12 Then came his disciples, and said unto him, Knowest thou that the Pharisees were offended, after they heard this saying?
Mat 15:13 But he answered and said,
Every plant, which my heavenly Father hath not planted, shall be rooted up.
Mat 15:14
Let them alone: they be blind leaders of the blind. And if the blind lead the blind, both shall fall into the ditch.
Mat 15:15 Then answered Peter and said unto him, Declare unto us this parable.
Mat 15:16 And Jesus said,
Are ye also yet without understanding?
Mat 15:17
Do not ye yet understand, that whatsoever entereth in at the mouth goeth into the belly, and is cast out into the draught?
Mat 15:18
But those things which proceed out of the mouth come forth from the heart; and they defile the man.
Mat 15:19
For out of the heart proceed evil thoughts, murders, adulteries, fornications, thefts, false witness, blasphemies:
Mat 15:20
These are the things which defile a man: but to eat with unwashen hands defileth not a man.
The issue that matters is the hearts of men. If one has an appearance of righteousness outwardly but whose heart is still corrupt then the appearance of righteousness means nothing, nothing at all. The appearance of righteousness is simply a witness to hypocrisy. At least an open sinner, without an appearance of righteousness, is not hiding something and is thus less likely to be self deceived when confronted with the truth.
A pure heart is intrinsically connected to a genuine faith. No pure heart = no genuine faith, for genuine faith purifies the heart (Act 15:9).