Many home exchangers are very happy to look after pets while on a swap but a few with allergies won't be able to do this. Even if a cat is not in the house during the period of the home swap, anyone with severe allergies won't want to stay in a house where the cat normally lives.
Make it clear in your description if anyone in your travelling party has allergies. Also read each listing thoroughly before contacting a member with your home exchange offer to ensure the home will be suitable. Most members with pets give details of their pets within their descriptions as well as often requesting and offering pet care.