FYI Illiberal values aka non-liberal values (clarifying because the I is hard to read) use the word liberal in the traditional sense.
Liberal values are liberty/freedom, consent of the governed, and equality before the law. All other liberal values build off of these three as a base. This implies that Non-liberal (or illiberal) values are the opposition of liberal values through censorship, gun control, etc like you mentioned.
Liberals in the modern US political sense refers to Neo-liberals. Neo-liberal and liberal are two very different things which is why the term liberal value doesn't necessarily correspond to neo-liberal beliefs.
Additionally, "the left" by and large does not support neo-liberalism. "The left" is violently against the aforementioned censorship, gun control, etc. Reading any socialist or communist literature will make this abundantly clear.
Examples:
- George Orwell on the Right to bear Arms: "The totalitarian states can do great things, but there is one thing they cannot do, they cannot give the factory worker a rifle and tell him to take it home and keep it in his bedroom. That rifle hanging on the wall of the working-class flat or labourer's cottage is the symbol of democracy. It is our job to see it stays there."
- George Orwell on Freedom of Speech: "Threats to freedom of speech, writing and action, though often trivial in isolation, are cumulative in their effect and, unless checked, lead to a general disrespect for the rights of the citizen."
- Karl Marx on the Right to bear Arms: "Under no pretext should arms and ammunition be surrendered; any attempt to disarm the workers must be frustrated, by force if necessary"
- Karl Marx on Freedom of Speech: "The absence of freedom of the press makes all other freedoms illusory. One form of freedom governs another just as one limb of the body does another. Whenever a particular freedom is put in question, freedom in general is put in question"
- Karl Marx on Freedom of Speech: "Censorship has outlived its time; where it still exists, it will be regarded as a hateful constraint which prohibits what is openly said from being written"
- Karl Marx on Freedom of Speech: "You cannot enjoy the advantages of a free press without putting up with its inconveniences. You cannot pluck the rose without its thorns!"
If you want I can dig up more quotes but those are the ones that were easy to fetch and any more risks turning this into even more of a wall of text.
My point being, your issues with "the left" are misdirected and are better focused towards Neo-liberalism and/or Neo-conservatism. "The left" does and has always been one of the primary guardians of liberal ideology. Hell "the left" is where a significant portion of the liberal ideology that the United States is founded on originated from.
All the experience the Chinese people have accumulated through several decades teaches us to enforce the people's democratic dictatorship, that is, to deprive the reactionaries of the right to speak and let the people alone have that right.
Those are great but the left in its current form pushes for larger and larger government. I believe that large government is incompatible with freedom. A hammer will always find a nail given enough time for bad actors to exploit the search space.
The left as it stands in its current dominant form, is a hypocrisy of incompatibles.
True liberalism as you describe it, doesn't exist in any first world country. It's been bundled into larger and larger government creep which inevitably tramples on individual rights.
The confusion seems to arise from Americans calling the democrats "the left". It's like fighting over which brand of chips is the best, Lays or Pringles.
Karl Marx quote on the right to keep and bear arms only applies to the proletariat. If you are a programmer and own the means of production (your laptop), you are not proletariat. All socialist and communist countries have strict gun control.
If you own AWS or GCP or Azure is a better example of owning means of production. A laptop cannot make you enough money to live by means of renting it out.
If you work for a living without owning the means of production and receiving the fruits of your labour, you are part of the proletariat.
If you own the means of production and receive the full fruits of your labour, you are part of the bourgeoisie.
Self employed programmers are bourgeoisie, employed ones are not. And of those that are part of the bourgeoisie, there are levels and not all of them are bad (even in the scope of socialist theory).
- The petite bourgeoisie are your small self employed shopkeepers, artisans, and tradesmen. These are the people who live by their own means and without exploiting anyone else's labour. Rising the proletariat to this level is the entire point of socialism.
- The moyenne bourgeoisie maintain largely the same lifestyle as the petite bourgeoisie but with strong financial establishment. They are effectively the upper end of the petite bourgeoisie and whether they are considered part of the problem or part of the end goal depends almost entirely on whether they are supported solely by their own labour or if they are unduly exploiting the labour of others. This class may lend money in some capacity however normally if they are doing so, they are doing it collectively.
- The grand bourgeoisie are largely where the problems with the bourgeoisie begin. These people have an established financial status from a few generations of wealth. This class is the one running larger businesses and their wealth is almost entirely derived from the work of others rather than their own.
- The haute bourgeoisie are the "true" bourgeoisie. You can only make it to this class through generations of wealth aggregation (unless you ride an industrial revolution) and once you are here, it is almost impossible to lose your financial status regardless of spending or financial failings. These are the eternally rich and their existence is only sustained by exploiting the labour of others.
Socialist theory considers the petite and moyenne bourgeoisie to be the "end goal" for society. They are nearly entirely sustained by their own labour and may use their excess funds to invest in the community (normally with some expectation of return but not any life sustaining amount). Marx warned that through the natural progression of capitalist society, these classes (primarily the petite but also the moyenne in some capacity) would wither while the wealth collected in the hands of the grand and haute bourgeoisie.
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Additionally, many socialist and communist nations have strict gun control not because they are socialist or communist, but because they are authoritarian. Gun control is a sign of authoritarianism more than anything else and any nation that falls towards it is going to see the population disarmed.