About the hadith: qualification and sources
The hadith quoted appears in al-Albanis as-Silsilah as-Sahihah which means he considers it as at least Hassan. My investigation so far ends with the conclusion that all earlier scholars pointed at issues with the narrator chain and therefore considered it as da'if as also displayed in the two versions appearing on sunnah.com:
"It is not for the believer to humiliate himself." They said: "How does he humiliate himself?" He said: "By taking on a trial which he can not bear."
(See in Jami' at-Tirmidhi and with a slight difference in Sunan ibn Majah)
Imam Ahmad, Al-Bayhaqi, Al-Bazzar, ibn Hebban, 'Abdurrazak and others have compiled the hadith with the wording of the version of imam at-Tirmidhi.
Many scholars have only quoted the first statement
"It is not for the believer to humiliate himself."
Among them at-Tabarani.
Imam Ahmad and ibn abi Hatim quoted it in their books on 'Ilal (issues) of hadith. The hadith is among the ahaad as ibn Abi 'Aasim compiled it in his book al-Ahaad wal Mathani (meaning: the ahadith which have been transmitted through one or two chains).
Ibn Abi Hatim says that Jundub (the young sahabi who heard Hudaifah) is rather added to the narrator chain and the hadith is better known as a mursal of al-Hassan (al Basri) beside the fact that 'Ali ibn Zayd ibn Jud'aan who heard from al-Hassan is considered as weak or even rejected by some scholars like ibn abi Hatim, ibn abi Shaybah, Ahmad and al-Bukhari as he has narrated some munkar hadith.
On the meaning of the hadith
Mulla 'ali al-Qarri said in his commentary called Mirqaat al-Mafateeh sharh Mishkat al-Masaabeeh مرقاة المفاتيح شرح مشكاة المصابيح:
When in the following I'm translating from Arabic without explicitly quoting a source these translations are of my own take them carefully!
( لا ينبغي ) : أي : لا يجوز للمؤمن أن يذل نفسه ) : أي : باختياره ، فلا ينافي ما ورد من أن المؤمن لا يخلو من علة أو قلة أو ذلة قالوا : ( وكيف يذل نفسه ؟ ) : وجه استبعادهم أن الإنسان مجبول على حب إعزاز نفسه ،
(It is not for) means: It is not allowed (for the believer to humiliate himself) means: by his own choice, so this doesn't contradict that a believer isn't free of defect or deficiency or humiliation (They said: "How does he humiliate himself?"): their disqualification (of this) is due to the human nature of loving to be valued.
( قال ( يتعرض من البلاء ) : بيان لما لا يطيق ، ... ومن العجيب ما ذكره ابن حجر قيل : بيان لما تقدم وهو أن يذل نفسه .
(He said: "By taking on a trial) is a clarification of (which he can not bear) and among the curious is what ibn Hajar quoted: it was said: it is a clarification of what was quoted before which is "humiliate himself"
Al-Mubarakpuri in his Thofat al-Ahwadi تحفة الأحوذي (the commentary of Jami' at-Tirmidhi) after identifying the narrators, said:
قوله : ( لا ينبغي للمؤمن ) أي لا يجوز له ( أن يذل ) من الإذلال ( قال يتعرض ) أي يتصدى ( من البلاء ) بيان مقدم لقوله ما لا يطيق .
The authors statement: (It is not for the believer) means it is not allowed for him (to humiliate) from humiliation (He said: "By taking on) means facing it (a trial) is a prior clarification for "which he can not bear".
He then added comenting at-Tirmidhi's comment which was not translated on sunnah.com:
قوله : ( هذا حديث حسن غريب ) في سنده علي بن زيد وهو ضعيف وإنما حسن حديثه الترمذي لأنه صدوق عنده وأخرجه أحمد أيضا من طريقه .
The authors statement: (This is a Hassan gharib hadith) is due to the appearance of 'Ali ibn Zayd in the chain who is da'if, and at-Tirmidhi only considered his narrations as Hassan because he is considered as sadoq (trustworthy to some extent) by him, and imam Ahmad has compiled it via the same narrator chain.
According to the fatwa on islamweb #99085 scholars have taken this hadith as an evidence that neither enjoining good and nor forbidding wrong الأمر بالمَعْرُوف والنَهي عن المُنْكَر is a due if one would bear oneself on taking a trial which one cannot bear!
This means if you have the choice you should avoid situations where you might put yourself in circumstances you may not be able to bear.