I agree that Civil Servants absolutely shouldn't strike in order to change policy or Governments. But it isn't clear that this is what's happening here. Note that the headline specifically says that Civil Servants "fear being forced to break the law", which is in breach of the Civil Service Code and explicitly overrides the duty to serve the elected Government.
Now, whether or not it's actually true that Civil Servants would be "forced to break the law", I don't know in this case. I was under the impression that the Rwanda Policy in general (albeit not in any specific case) had been ruled lawful in Courts, and the article isn't at all helpful in clarifying what the PCSU's spokesperson means. The Independent article linked below seems to expand on this, but the references to International Law don't seem to me to be any more persuasive as grounds to strike -- since, again, it ought to be for the Courts to determine the lawfulness of the policy, and they will surely have considered the position under International Law also.
The Telegraph article below says that Rwanda policy will come under review at the Court of Appeal shortly, so perhaps all this will change. Still, to the extent that Civil Servants should absolutely not be striking over *policy* matters, I wholeheartedly agree. But not every dispute is solely a matter of policy, and it's disheartening when they are characterised this way in order to disparage the Civil Service as a whole.
https://www.independent.co.uk/news/uk/politics/braverman-home-office-strike-rwanda-b2348421.html
https://www.telegraph.co.uk/news/2023/05/30/home-office-staff-threaten-strike-over-rwanda-policy/