Which character sets the tone of sympathy for Mrs. Wright?

Interesting question! It can be argued that the character who sets the tone of sympathy for Mrs. Wright is Mrs. Hale.
In the play, it is Mrs. Hale who takes control of the narrative by speaking up in defense of Mrs. Wright. When the county attorney makes a disparaging comment about Mrs. Wright's apparent lack of housekeeping skills, Mrs. Hale puts him in his place with a terse response: "There's a great deal of work to be done on a farm."
In the same conversation, the county attorney tries again by criticizing Mrs. Wright's use of "roller towels." Upon hearing this, Mrs. Hale counters with "those towels get dirty awful quick. Men's hands aren't always as clean as they might be."
In a later conversation with Mrs. Peters, Mrs. Hale defends Mrs. Wright's reputation again. Both women are discussing the possibility of Mrs. Wright having played a part in her husband's death. During the conversation, Mrs. Hale defends Mrs. Wright. She argues that a woman who worries about her canned fruit cannot possibly be a murderer as well.
In the play, we get further evidence of how Mrs. Hale sets the tone of sympathy for Mrs. Wright. It is Mrs. Hale who informs Mrs. Peters (and us) of how Mrs. Wright's marriage changed her. Mrs. Hale proclaims that the young Minnie Foster (before she became Mrs. Wright) used to wear pretty clothes and sing in a choir. Later, Mrs. Hale uses the adjectives "sweet," "timid," and "fluttery" to describe Mrs. Wright. These words are contrasted with her description of Mr. Wright, whom she calls a "hard man."
From the above, it can be argued that Mrs. Hale is the character who sets the tone of sympathy for Mrs. Wright.