Thinking about all the reasons for Nobunaga's selection of her Master in Redline, from the pettiness of her situation, to skipping over every single viable candidate, and instead picking the "least qualified" Master in the room, while still maintaining otherwise purely selfish motivations for participating in the grail war.
You could say it was a decision made of sympathies, but I think it's rather diminutive to suggest that's the only reason. After all, it's still a petty decision for a petty situation, to dismiss everyone who had just wanted to use you for their own gain and instead choose someone who did not. Likewise, for a selfishly motivated Servant, it's a also clear choice to pick someone who would not stand in your way or attempt to dictate your actions either. Sympathies or not, a Master paralyzed by fear with no clear goals of their own is easier to work with than one still seeking to use you, and it's not as though anyone would be able to openly protest the arrangement, either.
That said, it is not a purely selfish arrangement, just as it is not purely kindhearted. Nobunaga is still clearly protective of their Master, paying only her any regard while dismissing everyone else, and they do look after her between pursuing their own ambitions.
All that to say, for as cold and ambitious as Nobunaga is, they still hold sympathy for their Master, and for as protective as they are, they still have quite selfish motivations. There is complexity to their actions, and I both appreciate that and think considerably about it as well.