Under WA child support laws, will a anti harassment order against me by the child's father prevent me from seeking child support

If you read the order carefully, the order likely states that your are prohibited from contacting the protected person by any means through any person. However, there should be a stated exception for legal proceedings.

The existence of the order is not a legal obstacle in obtaining a parenting plan or an order of child support.

Remember that if the protected person contacts you, you should discontinue the contact immediately.

To protect yourself from any allegations of violating the order, you likely should be working with an attorney or the state's Child Support Services. Those offices will contact the alleged father on your behalf solely to resolve the legal issues.