Saki does not necessarily see herself as worse than a straight girl would be in her situation, but the fact that her first love was a woman and her current crush is a girl is pretty front and center in her introspection. She does not have to find her sexuality particularly abnormal for it to affect the way she views herself, even if through indirect means. We know at least that she tries to maintain the image of a straight girl.
There are definitely girls who nurture a crush for a male teacher and then later for a male friend, but Saki's situation is subtly different. Assuming that she is a lesbian, that makes her dating prospects more complicated. And if in her mind neither the piano teacher or Kanon were ever likely to return her feelings, they are kind of "safe" targets to love and keep loving; her relationships with them can satisfy some emotional needs without risking her image of normalcy. As long as Saki can sublimate her attraction into things like practicing the piano and being Kanon's friend, she does not have to try to date another girl and risk getting outed or otherwise hurt. Or, looking at it from the opposite way, if Saki is afraid to try dating another girl, that gives her an incentive to not try to move on from Kanon, and to keep nurturing a crush that in her mind can only ever be one-sided. Although simply being around Kanon all the time as her closest friend would make moving on difficult anyway.
On top of that, Saki has almost nobody to talk to about her feelings; she hides them from almost everybody she knows. Even if she has the most amazing mental defense against internalized lesbophobia, this has to feel pretty lonely.
So Saki's motivation to play the piano is "impure" because her reward is not just the music but an excuse to be around a girl/woman she likes. And her friendship with Kanon can be said to be "impure" in the sense that it has a dimension completely hidden from Kanon, which kind of puts a wall between them. Neither of these "impurities" are a direct result of her being gay and there are many other ways relationships and motivations can be compromised, but being gay is an important factor in why Saki's relationships have taken this shape with these particular hangups.