From a Jacobin article by Alexey Sakhnin who is a member of Left Front:

Like most politicians in modern Russia, Navalny’s worldview was formed under the total dominance of right-wing, market liberal ideology. In 2000, he joined the liberal Yabloko party. In those years, by his own account, he was a classic neoliberal, supporting a regime of low public spending, radical privatization, reduction of social guarantees, “small government,” and total freedom for business.

However, Navalny soon realized that a purely liberal politics has no prospect of success in Russia. For most people, this ideology was discredited by the radical reforms of the 1990s. It symbolized poverty, injustice, inequality, humiliation, and theft. And after pro-Western liberal ideology had lost so much luster in the eyes of the population, it ceased to be of interest to the ruling class either. Following Vladimir Putin, Russian officials, politicians, and oligarchs proclaimed themselves as patriots and true inheritors of the Russian state. Liberal parties turned out to be of no use to anyone.

Navalny soon found a new ideological niche. In the late 2000s, he declared himself a nationalist. He participated in the far-right Russian Marches, waged war on “illegal immigration,” and even launched campaign “Stop Feeding the Caucasus” directed against government subsidies to poor, ethnic minority-populated autonomous regions in the south of the country. It was a time when right-wing sentiments were widespread, and urban youth sympathized with ultra-right groups almost en masse. It seemed to Navalny that this wind would fill his sails — and partly, it worked.

But Navalny did not get lost among the petty nationalist “führers.” He found a special niche that made him a hero far beyond the boundaries of the right-wing radical subculture. He became the country’s main fighter against corruption. He would buy small amounts of shares in large state-owned companies and thus get access to their documents. On this basis, he conducted and published high-profile investigations. Many of them were brilliant journalistic work — though some critics suspected that Navalny was simply involved in the “media wars” among rival financial-industrial groups, receiving “orders” from them and information that compromised their competitors.

Navalny’s closest aide, Leonid Volkov, said in an interview that it was necessary to convince the Russian elite that an opposition victory would be better for them than a corrupt Putin government. But to do this, it was necessary to get rid of left-wing allies, who scared off big business. So Navalny split the oppositional coalition and when leftist leaders were thrown in jail, he declined to intercede on their behalf.

The Kremlin has always suspected that Navalny enjoys the tacit support of part of the elite. In 2012, the correspondence of some of the leaders of the liberal opposition was published, and it spoke of the possible financing of Navalny by a group of prominent oligarchs.

It is also important for Navalny that his criticism of social inequality does not turn the ruling establishment against him. Therefore, he is careful to make sure that his social populism does not overstep the line. Sharp criticism of the luxury of Putin’s entourage does not lead him toward radical social demands. Navalny is against revising the results of the criminal privatization of the 1990s or the redistribution of the national income in favor of working people. The most he agrees to is a small “compensation fee” that some oligarchs must pay to legitimize the property seized in the 1990s.

Inequality, then, will remain intact. Among the points of Navalny’s program on “fair courts” and political freedoms, there is also one on future privatization. And this is exactly what would likely alienate most Russians from him if it did reach the spotlight.

His People's Alliance party called for "drastically reducing government interference in the economy" in 2013. The Navalny-led party also called for stopping support for "rogue states" (basically socialist governments like Cuba, Venezuela, Nicaragua, Laos, China, and Vietnam as well as other governments like Iran, Belarus, and Syria that Putin's government had been increasingly economically supporting) and partnering up with Western countries.

In November of 2020, Navalny smeared indigenous socialist president of Bolivia Evo Morales who had been ousted in a far-right coup after winning a reelection:

The corrupt president, who illegally held power at the expense of lies and fabrications, fled the country.

Katya Kazbek, who is a fiercely anti-Putin Russian socialist writer, has a thread on Navalny's reactionary history that often gets ignored by Western coverage and also did an interview with Royce Kurmelovs that was posted at the Grayzone.