It's just a communication tool. Either it works for you personally, or it does not. I don't think it deserves a weekly HN first page discussion though.
At my current job I was asked to join a client's slack group (added without my consent) and it was a nightmare. The problems have nothing to do with notifications or interruptions, but it gives them the implicit understanding that I am a custom developer for their needs. Since they can reach me at any time, they assume that I am going to fix their bugs, add their features, etc. It circumvents what I think is the proper procedure for work. I suspect that's more the heart of why the author is saying they aren't going to join their client's slack group.
If you aren't their personal dev, then don't be one. The only thing my presence in a client's slack means is that I (and/or the other people from my company in their slack) am reasonable first point of contact. I'm perfectly happy telling them that their problem is not one I can solve (or choose to prioritize), and that they should touch base with <appropriate person>.
If I am ok to carry on this tangent we are already on, I cannot wrap my head around a scenario where it would be appropriate for a member of a SaaS company, dev/PM/CTO/QA or what have you to be in a slack channel for one of their clients. It's completely unprofessional and should be avoided.