To be fair most servants are dead set on winning for their own measure so obeying your master regardless of whom is sorta the normal thing to do
The difference is that Rider's goal
is to save Sakura. She isn't protecting Sakura because she wants to win, she wants to win because she wants to protect Sakura. Also, I said loyalty, not
obedience. Rider does
not obey Sakura unquestionably, there are several occasions where she goes against Sakura's orders because she thinks it's in her best interests. However, she does genuinely care for and love Sakura, and tries very hard to protect her.
To see the difference you only need to look at Rider's attitude towards
Shinji. She detests the guy, but she still obeys him because she wants to protect Sakura and she knows that, if she disobeys him, Sakura will pay for it. Plus, if she wins the war she can hopefully obtain freedom for Sakura. But, she has no issue with aiding Shirou in defeating him when he threatens Sakura, and nor is she particularly upset if he gets harmed.
saber is the same with shirou and lancer made kirei use a command spell to keep him from killing the priest
Well, Saber is the same with Shirou to a certain extent, yes, but Saber puts obtaining her goal first, at least initially. Hence why, if you don't get enough affection points for Saber in Fate, she ends up killing Shirou to obtain the Grail. Rider, conversely, is always protective of Sakura despite Sakura not really being in a position to protect or be affectionate towards
her.
As for Lancer, he just liked Bazett, because she was a hot chick and a cool fighting partner. As opposed to Kirei, who is a
dick who is trying to make him suffer as much as possible.
so its not like that loyalty is exclusive to rider
The distinction is that Rider's loyalty has
nothing to do with Sakura being her master. Even Saber is loyal to Shirou mainly because she's his servant, at least initially. In Rider's case she would be just as loyal and caring towards Sakura if she were summoned by someone else with the same knowledge and understanding of her plight.