Some have misconstrued that it prevents people from offering maintenance, support or professional services. This is a misreading of the language. Some have claimed that it conflicts with AGPL. Commons Clause is intended to be used with open-source licenses that are more permissive than AGPL, so that AGPL does not have to be used! Still, even with AGPL, few users of an author’s work would deem it prudent to simply disregard an author’s statement of intent to apply Commons Clause.
As far as I am able to understand the author, the specific claims being made here are:
Some have claimed that it conflicts with AGPL.
There exist some people who claim the AGPL "conflicts" with the Commons Clause. Assuming the author here means "is incompatible with" as the FSF uses the phrase, this is true: there do exist such people, and what is more, I think such people are right.
The Commons Clause adds restrictions not present in the AGPL. No GPL-family license admits the introduction of further restrictions on derivative or verbatim distribution, so you cannot distribute (or offer as a network service) combined AGPL-licensed and Commons-Clause-licensed work.
If the author means, "An original author cannot meaningfully release software under a license that contains the union of terms of the AGPL and the Commons Clause simultaneously," that may well be true, too, but it is largely semantics. See the final item in this answer.
Commons Clause is intended to be used with open-source licenses that are more permissive than AGPL, so that AGPL does not have to be used!
Code under the Commons Clause may be used alongside code under permissive FLOSS licenses. This is true; permissively-licensed code under MIT/X11 or BSD licenses can be used modified or unmodified within virtual any proprietary or freely-licensed code.
Still, even with AGPL, few users of an author’s work would deem it prudent to simply disregard an author’s statement of intent to apply Commons Clause.
This suggests to me that the author is discussing a case where a piece of software with a sole copyright holder is licensed under a custom proprietary license whose terms consist of both the AGPL and the Commons Clause. In general, a copyright holder may license their work under any terms they choose. However, the AGPL might be a nonsensical choice to couple with the Commons Clause, due to the language in Section 7:
If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term.
The Commons Clause certainly imposes further restrictions, so depending on how the copyright holder applies their license, they may be giving recipients free reign to drop the Commons Clause altogether by keeping this language from the AGPL in their license grant.
Of course it could be possible to retool the AGPL so it plays well with the additional restrictions of the Commons Clause, but then it obviously it wouldn't be the AGPL anymore. I think the final sentence you've quoted means, "This nonsensical pairing of restrictive terms and freedom to remove restrictive terms would lead to an unknown outcome in the legal system," which is certainly reason enough for me to avoid any software offered under such terms.