[Malleys]

var data = { action: 'sort_product', order: order, orderby: _this.data('orderby'), term: _this.data('term') };
$.ajax({
	url: "ajaxurl",
	type: "post",
	data: data,
	success: function(data){
		$("#loop").empty().html(data);
		var url = new URL(window.location);
		url.search = new URLSearchParams(data);
		history.pushState("", "", url);
	}
});

Но зачем пустое состояние??? Может лучше так?

var data = { action: 'sort_product', order: order, orderby: _this.data('orderby'), term: _this.data('term') };
$.ajax({
	url: "ajaxurl",
	type: "post",
	data: data,
	success: function(data){
		$("#loop").empty().html(data);
		window.location.hash = new URLSearchParams(data);
	}
});