I would like to make it clear in the beginning that I am going to be presenting my answer on the basis of English dubbed version of the movie of ‘Howl’s moving Castle.'
Sophie and Howl both had reasons to dislike the Witch of the Waste. Sophie despised the Witch of the Waste because she had put a spell on her that turned her into an extremely old woman. Her anger was quite prominent when she was unable to tell the truth about her spell and thumped her hands on the dining table and exclaimed, “If I ever get my hands on that Witch, I’m gonna wring her fat neck.”
Howl, on the other hand, was scared of The Witch of the Waste as she kept on hunting him down. He had explained the reason of this hunt to Sophie that, “she was once quite beautiful, so I decided to pursue her then I realized she wasn’t, so as usual I ran away,” therefore, he did not want to confront her.
Now it makes sense to find it a bit strange and confusing as to why these two characters had a change of heart and accepted her. Well, there are some of the following factors behind this.
Beginning with Sophie, as she was the one who had initiated the acceptance. After becoming an old lady, the first time she had met the Witch of the Waste was while going to the palace. Sophie did not wring her neck as she had exclaimed before because she was under the disguise of Howl’s mother and was trying to save Howl from going to the war. During the talk with madam Suliman in the palace, the Witch of the Waste was sucked out from all her powers, restored to her true old age and was brought sitting on a stroller into the hall of discussion. Sophie then realized the wicked intent of the invitations to the wizards by madam Suliman. When the Howl also entered in the hall and their disguise blew up, they flew away.
Sophie allowed the Witch to sit with them because of two reasons-
The Witch is now ripped off from all of her powers and has met her karma for her evil deeds. So, there is no need for Sophie wanting to take revenge on her. It is also made clear by the dialogue of madam Suliman that the Witch of the Waste was never evil from the beginning and she states, “Once she too was a magnificent sorcerer with so much promise, but then she fell to the prey of demon of greed who slowly consumed her body and soul. Hypothetically, it could be the similar type of contract as that of Howl’s with a demon but she might have unfortunately met a corrupt demon which then led to her demise. Secondly, Sophie has a kind heart and a forgiving nature. She knows how to move on from things and it is prominent in the manner she has managed and accepted to live inside the body of an old lady. Similarly, when she was overwhelmed and cried outside the castle, she maturely calms herself down and comes back to check upon Howl. These reasons suffice as to why Sophie spared the Witch of the Waste and didn't hold any grudge against her.
Howl, on the other hand, goes along with the decision of Sophie. He has asked Sophie when they flew away from the palace, “did you have to bring those two with you?” and Sophie shows her annoyance to the dog first and not to the Witch of the Waste and replies with “I can’t believe you work for Suliman. I guess it’s too late to toss them.” Howl shows indifference to this situation. They both then decide to let them flee away with them. Later on in the movie, due to the ongoing tension there was no time for them to talk over this issue again. The Witch is weak now; therefore, Howl seems to have no reason to fear from her anymore. Apart from this, he didn’t have any other ground to dislike her. In the ending part of the movie the loving nature of Sophie again appears as she hugs the Witch to make her let go off Calcifer from her hands implying in a way that she has accepted the Witch of the Waste as she is. There was no direct dialogue which elaborated that the Witch of the Waste had repented but it is implied through implicit actions, gestures that she didn’t intend to deeply hurt anyone. She has instead helped them by getting rid of the peeping bug which is sent by madam Suliman through Sophie’s mother. She even said, “I will never let Suliman get hold off Howl.” It could be both because she was possessive about Howl and had genuinely started to take care of him. Moreover, The Witch didn’t possess either any strong detestable traits or performed gruesome acts that would make it hard for Howl and Sophie to not forgive her. Afterwards, she was portrayed as a fun loving and flirty type of women. Hence, they both spared her and at the end accepted her as a part of the family as she was shown sitting in the balcony of the castle where the dog and Markl were playing.