In SCRUM technically it's the scrum master's responsibility to make sure everyone is participating in the process as they should. He will ultimatly have to answer if something goes wrong because of one team member's behavior.
Having said that, SCRUM also emphasizes the participation of the team as an important element of delivering good results. And obviously, Anne's behavor seems to bother you, so I think you should speak out.
I am finding it really demotivating from at least 2 points of view i.e.: 1) scrum master seems ineffective and 2) why should I care (I'm also a Scrum-cynic) if Anne doesn't and faces no consequences, maybe just because I'm newer to the org than Anne?
Whose behavior is bothering you, Anne's or the scrum master's? If Anne's behavior is bothering you, talk to her. If it's the scrum master's, talk to him. If it's both, talk to both. Maybe none of them has (yet) realized how you feel about it and telling them mightEventually though, someone will have an effect on their behaviorto talk to Anne. Even if it doesn't, at least nobody can say
The motivator behind people's actions is either that they didn't knowwant to gain something or that they are afraid to lose something. Anne's behavior might not be even rational, so understanding her motivations is necessary to adress her behavior.
WhenSince you share her scepticism of the SCRUM methodology it would not be a bad idea if you talk to themwith Anne instead of the scrum master, try to findsince you can start on a common ground which would make the right moment. That's what watercooler talk is (also) forconversation much less confrontational. InOnce you have established a more relaxed setting itconntection through your shared scepticism, you can start exploring the reasons for her behavior, which will be easierhelp you to find a way to get your message throughpoint across. With Anne it could be also helpful to ask
After you figured out her whymotivation, you might want to leave the SCRUM process bothers her so muchconversation at that her passive-aggressive behavior is warranted, soto give you can see whattime to think about your approach to the main motivators ofnext conversation with her behavior are.