If you think about how the economic system works, it will very quickly become obvious why this is the only way a leftist state can ever work : idea is that 2 things motivate people, one is richness and one is ideology. Since richness is taken away (that's the very goal of leftism), ideology is the one remaining. Given that, you cannot give freedom of ideology and expect something like communism to work. Even limited communism.
Assuming the goal of the left is still communism (even the ones of the "eventually" persuasion), I would still agree this is true, and therefore should have the "real" moniker.
In my opinion the "new left" has as a defining characteristic "globalism at any cost". The global free movement of people, and (because it's a necessity of movement of people) capital, and ideology is the central principle. This has somehow become what traditionally leftist parties stand for these days.
This is an extreme subversion of leftist thought, because, firstly, it is an extreme laissez-faire market idea, and should thus be classified as extreme-right. Secondly, it's self-destructive, as it allows the owners of means of production to use that movement of people, and especially to abuse it. Why ? To create ridiculous concentrations of wealth that are the very opposite of what leftism stands for. Needless to say, this abuse of people movement is happening on a large scale as a result. "Strongholds" of leftist thoughts (like the Bay Area and especially San Francisco) have become the main examples of what's wrong with capitalism, as gets frequently complained about on this very forum. And yet, most everyone from there professes to hold socialist ideals.
Even on a larger scale this is true. The republican party is currently about as left/right as the democrats (which is, I think, a large part of the reason for Trump's win), and democrats are moving to the right, republicans to the left. It's baffling to see, but every year requires more of a squint not to see it.
An other example would be collage kids. 30-40 years ago we had the political debate around private gender segregated college vs communal gender mixed college. The argument was that by mixing genders people will be more inclusive and less rigid in their group thinking. In modern left politics we instead see a lot of talk about women only school as an effective way to protect women and get more women into professions that is dominated by men. The idea is that they society should include them by giving them an exclusive safe space.
On the topic of religions I can also see a similar change in theme. Old left were more atheism leaning (through possible less so in the US) and regarded what people did in private as private and not part of group identity. Modern left is more focused in giving each religion equal space and promoting the different groups that self-identify as belong to one. It consider it especially important that society give each group the unique consideration that they need/demand.
The general theme here is that the old left either explicit or indirectly downplayed self-identified groups (gender, religions, and sexual orientation) by simply welcoming in everyone to join in the greater common goal (mostly against money/power in some version or other), and the group that did get promoted was the left movement itself. The right during this time acted in direct opposite by highlighted the multiple "others" in order to strengthen the self-group. Both the old and modern left movement focus on inclusion, but its the method used here and the side effects of those that is in stark contrast between new and old.