Is there a connection between pet and food allergies?

I am asking this question because we are traveling to a family lake house and we were told that pets are not allowed because of another family member's allergies.

The individual has strong allergic reactions to certain foods - i.e. peanuts and they discovered in testing that the individual is allergic to dogs as well (in a much lesser sense).

They are disallowing pets at the house because they were told that there is a negative cumulative effect of allergens on the immune system and that the person with the allergies would be more succeptable to a life threating allergy situation if they came into contact with pet dander due to the "unpredictable nature of potentially life threatening allergies".

I disagreed that a visit from a relatively hypoallergenic dog (a 7 lb tiny toy poodle that gets groomed every few weeks) several weeks prior to their visit could cause any reason for concern. The house will have plenty of traffic every week as different groups arrive and gets cleaned (dusted, vacuumed, floors mopped...etc. once a week).

They said they want to err on the side of caution by disallowing dogs. Is this being a little too cautious? Would the possibility of exposure to pet dander cause a potentially life threatening situation through "cumulative impact"?  The person does not have asthma.