There are some sisters who walk dogs that belong to their non-Muslim or non-practicing family members. They take the dogs for walks while wearing proper Islamic hijab. Is this permissible?

Keeping a dog is only allowed for hunting, for guarding livestock, or for guarding crops, and keeping one for any other reason is not allowed, for the Prophet ﷺ said that whoever keeps a dog other than for these loses of his reward each day (agreed upon). So when a dog is kept without such a need, helping to walk it and care for it is helping to maintain something that is not allowed, and it is better to keep away from taking part in it. As for touching, if she touches the dog while her hand and the dog are both dry, there is nothing upon her, but if there is wetness from its saliva on her hand or clothing, that spot is washed seven times, one of them with dirt. The hijab she wears is good in itself, but the concern here is the dog, not the covering.