A frame challenge here is determining what the "rights of the mobilized" means, which may be defined drastically differently depending on who you ask.
Even judging by the domain names, the prime aim of the listed services seem to be escaping mobilization and service, they may be somewhat successful at that, though realistically - crossing national border seems to be a much more reliable way to escape mobilization than going through it and then relying on NGOs to get you back. My scepticism is compounded by the observation that these NGOs seem to be more interested in Western press attention than in number of people they have successfully demobilized. Alignment with political opposition, who often flat out calls for non-compliance to orders and even sabotage, may also practically limit their legal results since they would be not viewed as faithful citizens with honest legal concerns.
However, there is a different direction of securing the rights of mobilized, such as, making sure that the mobilized are paid their wages and bonuses accordingly, that they are well equipped, that they are permitted leave they are due, that they get their compensation for being wounded, etc. People who were arguably mobilized without violation of law also need legal help. line of legal help also exists - I've heard that Junemann's OB has lawyers who take care of this, as well as some prominent mil Telegram channels. But the linked NGOs are very doubtfully will be interested in providing it, since their chief agenda seems to be evasion of military service, not improvement of military processes.
To illustrate, AGS "No War" (they're most socially active so I review them) started their Telegram channel shortly after the war has started by pulling a Tolstoi's quote directly denigrating servicemen
Война такое несправедливое и дурное дело, что те, которые воюют, стараются заглушить в себе голос совести. (Л. Толстой)*
War is such an unfair and bad thing that those who are fighting are trying to drown out the voice of conscience in themselves. (L. Tolstoi)*
following by a repost of Meduza article about them helping an anti-war activist.
* The caveat of this quote being that Tolstoi himself fought in a war, and the line was written in a diary when he was on active military duty, not trying to escape it by legal means - whether it applies to anti-war movement is debatable.