Assalaamu alaykum wa rahmatullaahi wa barakaatuhu, Shaykh. It is true that if a person does not implement what the person learns of the religious knowledge, then they are sinful. My question is about the knowledge outside the religion that one has, is it true for that too? I studied dental hygiene, hence if I do not implement what I learned and do not take care of my dental hygiene as much as a learned person can, then will I be sinful for it? And what about informing others about it too? I find that it is somehow linked to Islam as good hygiene is part of our religion, ut it is not religious knowledge in itself. May Allaah reward you, Shaykh.

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.

In principle, it is permissible to refrain from acting according to a worldly science that someone had learned, unless refraining from acting on it causes harm to one’s own self or other Muslims, because worldly sciences such as medicine, engineering, and others are among the communal sciences, which are not obligatory on every adult, but it may be obligatory on some adults if there is no one else to carry it out.

Shaykh Ibn Taymiyyah said in his book Al-Hisbah:

“The acts that are communal obligations become an individual obligation if no one does them, especially if other people are unable to do them. So if the people are in need of the farming of a people or their weaving or their building, then this kind of work becomes obligatory (i.e. a communal obligation), and the ruler obliges them to do it if they refrain from doing it in return for wages equivalent to the job, and he should not let them ask the people to pay them more than the equivalent wages, and he should also not allow the people to oppress them by giving them less than their right.” 

The ruling on teaching worldly sciences or not teaching them is the same as the ruling on acting according to them, with the details mentioned above.

As regards your question, "Will I be sinful for not taking care of my dental hygiene, despite my knowledge of the importance of taking care of it?"

The answer is based on the harm caused to your teeth because of neglect. The ruling about this is the ruling of seeking treatment or not seeking treatment. The fact that you have learned dental hygiene does not affect the ruling of neglecting it in the Sharia, but this is blameworthy in the custom of the people.

The Islamic Fiqh Council's decision on seeking treatment reads:

Rulings on medical treatment vary according to the situations and persons involved:

A. It is obligatory if forgoing it may result in a person’s death, loss of an organ, or disability, or if the illness would spread to others, as in the case of contagious diseases.

B. It is recommended if forgoing it may weaken the body without entailing the consequences mentioned in the first case above.

C. It is permissible if not covered by the preceding two cases.

Allah knows best.