Possible for worldling to practice the Ariyamagga, to walk it?

No.

The Noble Path includes celibacy plus entering the path actually requires stream entry first. MN 117 says about the path that is "noble" that "Right View" is the leader or forerunner.

For example, about developing jhana, the Buddha taught (in SN 48.9 & SN 48.10) the noble disciple makes 'letting go' ('vossagga') the object of meditation. If 'self' cannot be let go of & abandoned, even developing jhana is difficult (because even samadhi can dissolve the self construct and the self instinct can fight back against the samadhi dissolution stream).

This is why, on certain chat sites, there are always posts about the over-estimated attainment of what is imagined to be 'jhana'. Some minds experience some samadhi and some momentary bliss but because ego self cannot dissolve, the opposite to dhamma occurs. These minds spend the rest of their life claiming their "self" attained jhana. They can even become famous jhana-lite teachers; particularly if they are Americans or Jews socially conditioned from youth to talk & boast a lot.

Because we are noble practitioners who practise noble right speech, we will not disclose these chat sites or fake jhana-lite gurus. MN 117 says the noble practitioners desist from wrong speech that creates internal & external self-views of imaginary "beings". SN 5.10 says only Mara believes in "beings"; that, in reality, there are no "beings" to be found. All that can be found by the luminous clear mind is aggregates (khandha), elements (dhatu) & sense objects (ayatana).

[Note, this question is thought to not keep one to where he/she is bound; to offer release from clinging to the world of illusion & creating the illusion of "beings to be saved" and to go beyond and join the Noble Sangha or Noble Dhatu. There is not much time left for ego self to die before dying]

A person needs right view, but he doesn't need to be a stream entrant to follow the Noble Eightfold Path.

He needs to be either a faith follower or Dhamma follower according to MN 70 (below).

A faith follower may not have perfect right view, but he needs to improve his understanding of the Dhamma through reflecting on them sufficiently with wisdom, in order to become a Dhamma follower. A faith follower is obviously not a stream entrant.

Is a Dhamma follower necessarily a stream entrant? - that's a good question to ask. Perhaps I will ask this.

“What kind of person is a Dhamma-follower? Here some person does not contact with the body and abide in those liberations that are peaceful and immaterial, transcending forms, and his taints are not yet destroyed by his seeing with wisdom, but those teachings proclaimed by the Tathāgata are accepted by him after reflecting on them sufficiently with wisdom. Furthermore, he has these qualities: the faith faculty, the energy faculty, the mindfulness faculty, the concentration faculty, and the wisdom faculty. This kind of person is called a Dhamma-follower. I say of such a bhikkhu that he still has work to do with diligence. Why is that? Because when that venerable one…into homelessness. Seeing this fruit of diligence for such a bhikkhu, I say that he still has work to do with diligence.

“What kind of person is a faith-follower? Here some person does not contact with the body and abide in those liberations that are peaceful and immaterial, transcending forms, and his taints are not yet destroyed by his seeing with wisdom, yet he has sufficient faith in and love for the Tathāgata. Furthermore, he has these qualities: the faith faculty, the energy faculty, the mindfulness faculty, the concentration faculty, and the wisdom faculty. This kind of person is called a faith-follower. I say of such a bhikkhu that he still has work to do with diligence. Why is that? Because when that venerable one makes use of suitable resting places and associates with good friends and nurtures his spiritual faculties, he may by realising for himself with direct knowledge here and now enter upon and abide in that supreme goal of the holy life for the sake of which clansmen rightly go forth from the home life into homelessness. Seeing this fruit of diligence for such a bhikkhu, I say that he still has work to do with diligence.

Sutta. Ma. U. Dakkhiṇāvibhaṅgasuttaṃ:

Ānanda, of an offering made to an animal the results expected are by hundreds. Of an offering made to an ordinary not virtuous person the results expected are by thousands. Of an offering made to an ordinary virtuous person the results expected are by hundred -thousands Of an offering made to a not greedy one, turned away from sensuality the results expected are by hundred thousand millions. Of an offering made to a person fallen to the method of realizing the state of entry into the stream of the Teaching, the results expected are innumerable and unlimited. What would be the results for offering a gift to a stream entrant of the Teaching? Or one fallen to the method of realizing the state of not returning? Or one who would not return? Or one fallen to the method of realizing worthiness? Or a worthy disciple of the Thus Gone One? Or the silent enlightened One? Or the worthy, rightfully enlightened Thus Gone One?

It's Atthakatha:

"a person fallen to the method of realizing the state of entry into the stream of the Teaching" means at least a(n ordinary) upāsaka who goes to the Three Gems for refuge.

Why the ordinary upāsaka is included?

As I explained it here:

It is similar to when you are following an expert guide and you are going to arrive the right destination surely, no one can't say "you are going the wrong way" although you do not understand the map by yourself at first.

However the ordinary is included only when he still trust in the three gems.

Briefly, no, it is not possible to hold onto wrong view and expect progress on the Path. See AN8.29:

Furthermore, a Realized One has arisen in the world. And a person is reborn in a central country. But they have wrong view and distorted perspective: ‘There’s no meaning in giving, sacrifice, or offerings. There’s no fruit or result of good and bad deeds. There’s no afterlife. There’s no obligation to mother and father. No beings are reborn spontaneously. And there’s no ascetic or brahmin who is well attained and practiced, and who describes the afterlife after realizing it with their own insight.’ This is the sixth lost opportunity …

DN33 has a similar passage and lists wrong view as the seventh lost opportunity.

Your own quote in the OP says much the same.

While the Buddha teaches right conduct for best and happiest dwelling and wandering on in the world for those not seeing the dangers in the world, i.e. suffering and stress, this Dhamma and religion at it's heart, the Dhamma of the Ariya, is not one graspable for ordinary people. It's the path of the Noble Ones, the path of wisdom and compassion, the path of goodness in a forest of blindness and defilments, an even path under the uneven, right between the tracks of corruption.

There is the case where a son of good family realizes: "This homelife is a dirty and dusty road..." and looks after The Fruits of the Contemplative Life.

As for those believing that pulling the heritage of the Noble Ones into their world, suggesting that all are worthy and ready for hot-dogs and creat their specials, disregard the wise, elders, contemplatives, not only that they actually walk themselves for a poor lifelihood toward degeneration but also work for the long term pain and suffering of many.

Only if one is honest in regard his/her incapacities and comes to really take refuge to those and that on a real Ariya Domain, only then one could be guided toward a borderland and the door to the Noble path leading to the deathless and end of all suffering and stress.

Householders are wise if seeing their all is on fire, lower their heads and seek for escape following those walk, having walked a tiny path.

Sadhu OyaMist for the try to share, "sadly" this teachings are already occupied by the worlds greates thieves, and lost to be given at the right time for those ready to receive. The "We have right"-leaders of "red (marxist) buddhism", those with grave wrong view and ingratitude and disrespect toward the Noble Ones and the Gems.

[Note: this is not given for trade, exchange, stacks, and whatever binds but for release, for a tiny door of escape]

OP: People with wrong view often try to practice the Noble path

This is impossible because right view is the first step in noble eightfold path.

OP: Is it actually possible or doesn't it require stream entry first?

It's not required someone to attain stream entry first in order to practice noble eightfold path. Actually noble eightfold path is what leads a sentient being towards stream entry.

Note: This is what I understood. I may be wrong but not Dhamma.

I think that to ask "Is it possible for a worldling to walk the path?" is similar to asking "Is it possible for a person to become enlightened?"

I think the usual answer to the latter question is that enlightenment isn't personal and that notions of being a person aren't helpful, they're even a hindrance.

But the way the question is phrased -- "people with wrong view" -- sounds definitive, doesn't it.

I suppose it's useful to distinguish right from wrong view, maybe less helpful to judge people like that, to associate that with people, to condemn people, judge them, to assume they can't learn, and so on.

Imagine being a school teacher at the beginning of the year, and asking "Can these students pass the end-of-year exam?" An answer might be, "No they can't" -- because they haven't learned (haven't been taught) the subject yet, and therefore maybe can't practice properly either -- but that isn't the right way to see people (students).

From there I guess there's doctrine about buddha-nature or the seed of enlightenment, including Joshu's Dog

Has a dog Buddha-nature?
This is the most serious question of all.
If you say yes or no,
You lose your own Buddha-nature.

The answer might be obvious, but the last line suggests that the question wasn't about the dog.