The Japanese translation is grammatically incorrect and sounds very unnatural. Let me explain each flaw in the original translation. You’d better just ignore this broken sentence.
1 Wrong tense
彼は私が忠告するからといって should be 彼は私が忠告したからといって. 忠告するからといって in this particular context can be only interpreted as “although I am going to give warnings”. It’s not happened yet.
2 Wrong comparison
それだけ should be removed from this sentence (the best option), or at least replaced with それほど (the better and more natural option). それだけ in general means either “as much as” or “to that extent”.
それだけ in this particular sentence compares A) the degree of diligence that I expected to him, and B) the degree of diligence that he actually demonstrated after my warnings. But the original English sentence compares C) pre-warning and D) post-warning. Being below my expectation doesn’t always mean he didn’t improve his behavior at all.
If the original sentence also compared A and B, それだけ is still very unnatural. It should be それほど (not so much as (I expected)). It’s a matter of collocation.
という is inserted to slightly emphasize the meaning of “not always result in”. In many of the cases, you can drop という without significantly changing the original meanings.
マスクをしたからといって (or しているからといって）、コロナに感染しないわけでもない。
マスクをしたからといって (or しているからといって）、コロナに感染しないというわけでもない。
These two sentences means the same: “Wearing a face mask doesn’t always prevent us from infection by corona virus.”
わけでもない is also spelled as 訳でもない. 訳 means “a reason”, “a motivation” or “a root-cause”. 訳でもない, therefore, picks up a cause and an effect, and then means that the cause doesn’t result in the same effect.
- 感染しない (not be infected) + 訳 (root-cause) + でもない (not always be so).
- 感染しない + という (not BEING infected) + 訳 (root-cause) + でもない (not always be so).
Inserting という turns a verb into a gerund (noun verb) in order to bridge another noun “訳”.
The problem here is that the original Japanese author from Tatoeba uses ～というわけでもない to describe the relationship between the cause (my warnings) and the effect (his diligence). ～というわけでもない for this particular context treats him like an animal or an inanimate object/situation. It makes the whole sentence sound rude and unnatural. Omitting ～という doesn’t solve the problem at all.
Here is my alternative translation:
忠告 means “advice”. We, Japanese, generally avoid saying 警告 when we merely wish someone to improve his/her behavior. The only situation you can use 警告 is when you give someone an order to comply with laws and rules. In other words, disobeying 警告 often leads to punishment. My second translation with 警告 is suitable when you give a lay-off warning to your subordinate.
相変わらず means “be still”, “unchanged”. So, 相変わらず compares the change in his diligence pre- and post- warning.
怠慢だ means “be lazy”, “not hardworking”. It can be used in academic and also in professional situations.
本腰を入れる is a frequent idiom, literally meaning "insert your own waist. When you lift a heavy box, you need a physical power around your waist. So, 本腰を入れる means “to become more serious and concentrate on something”. It also highlights the difference of his diligence pre- and post-warning.