Anyone with atom's weight of arrogance will not enter paradise. But Allah forgives minor shirk if repented. Is arrogance more dangerous than shirk?
Bismillah Hir Rahmaan Nir Raheem
As Salaamu 3laykum,
I hope you are doing well. We have to understand the main backbone of Islam is based on our intentions. Even my typing this answer is being judged.
I heard ALLAH Messenger (ﷺ) saying, "The reward of deeds depends upon the intentions and every person will get the reward according to what he has intended. So whoever emigrated for worldly benefits or for a woman to marry, his emigration was for what he emigrated for." (Bukhari, chapter of Revelation)
The hadith you had mentioned is this:
"Whoever has a mustard seed's weight of pride (arrogance) in his heart, shall not be admitted into Paradise. And whoever has a mustard seed's weight of faith in his heart, shall not be admitted into the Fire." (Tirmidhi)
But to understand this hadith is that the person will cleansed/forgiven before entering paradise. To show that there is no enmity, jealousy, arrogance in heaven.
Furthermore, when it comes to shirk there are two types, major and minor. Major shirk is associating anything with ALLAH (Glory Be to HIM).
Surely those who disbelieve, hinder ˹others˺ from the Way of Allah, and then die as disbelievers; Allah will never forgive them (Surah 47 verse 34)
Now when it comes to minor shirk here is the hadith that states the details.
The Messenger of ALLAH (peace and blessings of ALLAH be upon him) said: “The thing that I fear most for you is minor shirk.” They said: “O Messenger of ALLAH, what is minor shirk?” He said: “Showing off, for ALLAH will say on the Day when people are recompensed for their actions: ‘Go to those for whom you were showing off with your deeds in the world, and see what reward you find with them.’” Classed as saheeh by al-Albaani in al-Silsilah al-Saheehah, 951.
Major shirk is never forgiven. When it comes to any other sin it can be forgiven. Now when comparing minor shirk and arrogance they are both sins and we should refrain from both of them.
Have a nice day!