Why did Mrs. Beale extend her friendship and hospitality to Maniac?

Mrs. Beale knows that Jeffrey Magee has nowhere to go, and she does not care that he is white.

Amanda brings Jeffrey home, and he just sort of stays. He stays for dinner, and then does not leave. When Mr. Beale tries to drive him home, he asks to be let out in the East End. Mr. Beale knows that is not his house, because Maniac is white and the whites live in the West End. 

Mr. Beale made a U-turn right there and headed back. Only Mrs. Beale was still downstairs when they walked into the house.  She listened to no more than ten seconds' worth of Mr. Beale's explanation before saying to Maniac, "You're staying here." (Ch. 12) 

Maniac is thrilled to be staying with the Beales. They are good people. They have a stable home. For the first time since he ran away, Maniac has a real address. He finally has a family again. 

Amanda gives Maniac her room, and she does not mind at all. She would much rather sleep with her little brother and sister. They bother her during the day, but she likes cuddling with them at night.

Amanda was happy to give up her room to Maniac. It gave her an excuse to sleep with Hester and Lester every night. ... [At] night, the best thing was to have them snuggled up on both sides of her. It made no sense, but that's how it was. (Ch. 13)

Unfortunately, not everyone is as happy as the Beales that Maniac is staying with them. Many people just do not understand a white boy living in the East End. Maniac leaves, reluctantly. He lives with an old man, Grayson, at the zoo bandshell for awhile. When Grayson dies, he goes back to live with the Beales for good.