Daenerys' arrival will have many layers to it for the different houses and actors who confront her.
For House Lannister, it is conflicting with the house they always aspired to be. They wanted to marry into House Targaryen, practiced both incest and their doctrine of their house's supremacy. House Targaryen was the only house they envied, the exception to Lannister supremacy.
On an individual level, for Jaime, it means confronting his past. He confronts his crime that earned him the name "Kingslayer" that ended his efforts to be a true knight like his mentor Arthur Dayne, and with it the question of where he stands now. For Cersei, Daenerys is both what she aspires to be as a ruling queen: an absolute monarch with the monopoly on violence firmly in her hand making her stronger than any man, and her foil in that both are abuse victims sold into marriage but Daenerys rejects her family's doctrine of supremacy while Cersei embraces it. For Tyrion, it means abandoning his father's toxic legacy and finding the balance between realpolitik and his fondness for "cripples, bastards and broken things."
For House Baratheon, it means confronting the house they overthrew now that they are the ones who were usurped. Stannis faces another claimant for Azor Ahai who unlike him hatched actual dragons and whose claim to the throne supersedes his own. Daenerys is the image of who he thinks he is in a way that would make him question his own role. She essentially wrecks his story.
For House Martell, Daenerys represents two parts of their heritage. Daenerys is the image of their forebear and founder of the Dornish kingdom Nymeria: an Essosi warrior queen leading her people from slavery to Westeros. She also bears the name of the Targaryen ancestor of House Martell who continues to bear considerable influence on the family. Like the original Daenerys, Dany was married off to a foreign ruling sovereign as part of an alliance, and carries her concern for the common people.
Daenerys Targaryen, Maron's wife, was the one for whom the Water Gardens were built and she was the one who came up with the lesson in ruling made form observing the children playing in the pools that she instilled into her son that continued to be passed down to the generations all the way to Doran. Arianne looks at her portrait when she was a child constantly praying to be beautiful rather than her lesson, seeing Targaryen as something to aspire to.
In fighting Daenerys, they would be warring against the image of their family's legacies and heritage for the sake of a crown, pride and vengeance. It is also Arianne fighting against the image of her personal ideal.
For the High Septon, Daenerys is the embodiment of everything he opposes. She is a savior of another faith, the Red Faith, like Stannis. Like Cersei, Daenerys is also a ruling queen which doesn't sit well with the High Sparrow's misogyny. Daenerys also bedded horselords (nevermind that she wasn't given a choice) and had other partners, adding more fuel to his misogyny given his views on women and premarital sex. Like Cersei's children, she is a product of incest which the Faith abhors, and makes her an abomination by birth. Finally, she has dragons which were essential tools in crushing the power of the Faith. She would present a clear threat to his newly acquired military and political power.
For House Stark, the person it will most likely effect is Jon Snow. Jon will have learned the truth of his paternal heritage and struggling with this information and identity. Daenerys to Jon is acknowledging this information of being a scion of House Targaryen and deciding where to go with the knowledge of his newfound identity. Confronting Daenerys is essentially Jon confronting and accepting his Targaryen identity.
