The first thing to note is that arguably the FIDE Laws of Chess do not apply.
The introduction spells out their limitations:
FIDE Laws of Chess cover over-the-board play. The Laws of Chess have two parts: 1. Basic Rules of Play and 2. Competition Rules.
Arguably they only cover behaviour while playing over the board. Hence article 11.1 does not apply.
11.1 The players shall take no action that will bring the game of chess into disrepute.
FIDE does have codes of ethics. There are two published documents, one covering the period up to April 2022 and one the period after.
The current code, Code of Ethics effective till 1 April 2022, was originally written in 1989 and amended in 1996 and mainly covers chess play and chess politics.
- Breach of Ethics
The Code of Ethics shall be breached by a person or organization who directly or indirectly
2.1 offers, or attempts to offer or accepts any consideration or bribe with a view of influencing the result in a game of chess or election into FIDE office.
2.2 in other respects acts contrary to this Code.
There follows a list of competition related items, but at the very end we have the "ethics" equivalent of 11.1:
2.2.10 In addition, disciplinary action in accordance with this Code of Ethics will be taken in cases of occurrences which cause the game of chess, FIDE or its federations to appear in an unjustifiable unfavorable light and in this way damage its reputation.
2.2.11 Any conduct likely to injure or discredit the reputation of FIDE, its events, organizers, participants, sponsors or that will enhance the goodwill which attaches to the same.
Regarding Karjakin and Shipov, The Official Statement of FIDE Council states:
In order to safeguard FIDE from reputational, financial, and any
other possible risks, FIDE terminates all existing sponsorship
agreements with any Belarusian and Russian sanctioned and/or
state-controlled companies and will not enter into new sponsorship
agreements with any such companies.
FIDE Council condemns any public statement from any member of the chess community which supports unjustified military action and brings the case of chess grandmasters Sergey Karjakin and Sergey Shipov to the Ethics and Disciplinary Commission
So, it would seem that the statements of support for Putin and the military action by Karjakin and Shipov are regarded by FIDE as possibly putting FIDE at risk of reputational damage and hence these break the FIDE code of ethics.
Edit 22/3/22: FIDE have now published their verdict on Karjakin and Shipov confirming this:
Sergey Karjakin is found guilty of breach of article 2.2.10 of the FIDE Code of Ethics, and is sanctioned to a worldwide ban of six months from participating as a player in any FIDE rated chess competition, taking effect from the date of this decision, 21 March 2022.
Sergei Shipov is found not guilty of breach of article 2.2.10 of the FIDE Code of Ethics.