Generally speaking, it does not mean that you need permission to attend activities during the other parent's residential time.
It is possible that the language of your particular parenting plan could say something else. Especially if you and the other parent created the parenting plan by agreement. You should read it carefully and/or speak with an attorney to determine if this is the case.
If there is a protection order/restraining order in place that restricts contact with the children or the other parent, the parent subject to the order should seek legal advice before seeking contact with the children that is not expressly granted in the parenting plan.
You should review the "Alternative Dispute Resolution" provisions of your Plan and consider initiating mediation, arbitration or other ADR designated in the Plan. As I understand it, the other parent believes that you should be excluded from school and other child activities on the "other parent's" time. If your Plan is silent on this issue, and there are no legal restraining orders in place, this strikes me as a "plan implementation" issue best addressed by ADR. In fact if it is an "implementation" issue and there IS an ADR provision (towards the end of your WA Plan) you would be required to attempt to solve the problem by ADR before asking a court for relief.