Quran 19:71 does not require the belief that every Muslim must first be punished inside Hell. The strongest mainstream reading is that all people will come to the Fire's vicinity and pass over it, while the God-fearing are saved from entering it as a place of punishment.
Why the objection seems forceful
The objection has a real point: the verse uses universal language - "there is none of you but will come to it" - and then says, "We will save those who feared Allah." Read quickly, this can sound as though every person first enters Hell and only some are later removed. That would seem to conflict with descriptions of the righteous being admitted to Paradise and with Allah's promises of protection.
There is none of you but will come to it. This is, with your Lord, a decree that must be fulfilled. Then We will save those who feared Allah and leave the wrongdoers therein on their knees.
Quran 19:71-72
What "come to it" means
The Arabic verb warada means to come to, approach, or reach a place. It does not always mean to enter and remain inside it. The early exegetes therefore explained this passage in more than one closely related way: people will approach Hell, see it, or cross over it. The well-known explanation in classical tafsir is the crossing over the Sirat, the bridge placed over Hell.
This understanding is supported by another Quranic statement:
Indeed, those for whom the best has already gone forth from Us - they will be kept far away from it. They will not hear its sound, while they are abiding in what their souls desire.
Quran 21:101-102
If 19:71 meant that every righteous person must literally enter the Fire and suffer there, this promise would be difficult to reconcile with it. But if "coming to it" includes passing over it or being brought before it, the verses fit together naturally.
How the Sunnah explains the passage
Authentic reports describe the believers crossing the bridge over Hell at different speeds, according to their faith and deeds. Some pass like lightning, while others are caught and then delivered by Allah's mercy. The Prophet Muhammad (PBUH) also described intercession and Allah's rescue of people from the Fire. These reports explain the "coming" and the "saving" without making punishment the first destination of every Muslim.
Then the bridge will be set over Hell, and intercession will be permitted. They will say, "O Allah, save us, save us."
Sahih al-Bukhari and Sahih Muslim
What the verse does and does not establish
It does establish that the Hereafter includes a terrifying encounter with Hell and that no one should rely on a label or claim while neglecting faith and repentance. It does not establish that every Muslim must be thrown into Hell before reaching Paradise. A believer who is forgiven enters Paradise without punishment; another may be punished for sins; and the righteous are protected by Allah. Their "direct entry" means entry without being detained in the Fire, not exemption from the final crossing and judgment.
Thus the passage is a warning, not a denial of hope. Allah saves those who are mindful of Him, and His promise of Paradise remains true.