Should the Left move away from identity politics if they hope to fight illiberalism?

There’s no denying that identity politics have taken a front-line position in Left wing ideology in the West at this time. I recently read an interesting article written by a woman who identifies as Left-wing but resents the post-modern identity-politics that have overtaken the wing:

https://areomagazine.com/2017/03/27/how-french-intellectuals-ruined-the-west-postmodernism-and-its-impact-explained/

I can’t expect everyone here to read this article in full, nor am I claiming this article isn’t without problems, but I think it’s an interesting read and worth discussing. Essentially the author argues that the post-modern emphasis on identity has caused us to move away from concern with universal human issues (freedom, rights, etc. things that were once considered “liberal”) and focus on individual experience framed by race, gender, etc. Thus there is an increased cultural relativism, and a shying away from Enlightenment values like humanism, liberalism, science and reason, which are now framed as oppressive/bourgeois/masculine.

Quoted from the article: “The Left is not responsible for the far-Right or the religious-Right or secular nationalism, but it is responsible for not engaging with reasonable concerns reasonably and thereby making itself harder for reasonable people to support. It is responsible for its own fragmentation, purity demands and divisiveness which make even the far-Right appear comparatively coherent and cohesive.”

So then this preoccupation of the Left is alienating people, clouding their message, and allowing the far right to prosper. What should the left do in response?

I know this is a wall of words, but I’m trying to include the important parts. This is a general discussion. Any comment you wish to make on this topic, go ahead and make it.