diff --git a/packages/babel-parser/src/parser/expression.js b/packages/babel-parser/src/parser/expression.js
index f67d56160d64..2e0cf1a22b95 100644
--- a/packages/babel-parser/src/parser/expression.js
+++ b/packages/babel-parser/src/parser/expression.js
@@ -1204,29 +1204,7 @@ export default class ExpressionParser extends LValParser {
         return this.parseTopicReferenceThenEqualsSign(tt.bitwiseXOR, "^");
       }
 
-      case tt.doubleCaret: {
-        const pipeProposal = this.getPluginOption(
-          "pipelineOperator",
-          "proposal",
-        );
-        const pluginTopicToken = this.getPluginOption(
-          "pipelineOperator",
-          "topicToken",
-        );
-
-        // The `^^` token is valid only when:
-        // the pipe-operator proposal is active,
-        // its "pipeProposal" is configured as "hack",
-        // and "topicToken" is configured as "^^".
-        // If the pipe-operator proposal settles on a token that is not ^^,
-        // then this token type may be removed.
-        if (pipeProposal === "hack" && pluginTopicToken === "^^") {
-          return this.parseTopicReference(pipeProposal);
-        } else {
-          throw this.unexpected();
-        }
-      }
-
+      case tt.doubleCaret:
       case tt.doubleAt:
       case tt.bitwiseXOR:
       case tt.modulo:
diff --git a/packages/babel-parser/src/tokenizer/index.js b/packages/babel-parser/src/tokenizer/index.js
index 699a51691533..9af4cf036c75 100644
--- a/packages/babel-parser/src/tokenizer/index.js
+++ b/packages/babel-parser/src/tokenizer/index.js
@@ -715,10 +715,6 @@ export default class Tokenizer extends ParserErrors {
 
   readToken_caret(): void {
     const next = this.input.charCodeAt(this.state.pos + 1);
-    const pipeProposal = this.getPluginOption("pipelineOperator", "proposal");
-    const topicToken = this.getPluginOption("pipelineOperator", "topicToken");
-    const hackPipeWithDoubleCaretIsActive =
-      pipeProposal === "hack" && topicToken === "^^";
 
     // '^='
     if (next === charCodes.equalsTo && !this.state.inType) {
@@ -728,11 +724,15 @@ export default class Tokenizer extends ParserErrors {
       this.finishOp(tt.xorAssign, 2);
     }
     // '^^'
-    else if (hackPipeWithDoubleCaretIsActive && next === charCodes.caret) {
-      // `tt.doubleCaret` is only needed to support ^^
-      // as a Hack-pipe topic token.
-      // If the proposal ends up choosing a different token,
-      // it may be removed.
+    else if (
+      next === charCodes.caret &&
+      // If the ^^ token is not enabled, we don't throw bug parse two ^s
+      // because it could be a ^ hack token followed by a ^ binary operator.
+      this.hasPlugin([
+        "pipelineOperator",
+        { proposal: "hack", topicToken: "^^" },
+      ])
+    ) {
       this.finishOp(tt.doubleCaret, 2);
 
       // `^^^` is forbidden and must be separated by a space.
@@ -751,11 +751,13 @@ export default class Tokenizer extends ParserErrors {
     const next = this.input.charCodeAt(this.state.pos + 1);
 
     // '@@'
-    if (next === charCodes.atSign) {
-      // `tt.doubleAt` is only needed to support @@
-      // as a Hack-pipe topic token.
-      // If the proposal ends up choosing a different token,
-      // it may be removed.
+    if (
+      next === charCodes.atSign &&
+      this.hasPlugin([
+        "pipelineOperator",
+        { proposal: "hack", topicToken: "@@" },
+      ])
+    ) {
       this.finishOp(tt.doubleAt, 2);
     }
     // '@'