diff --git a/packages/angular/build/src/tools/angular/compilation/parallel-compilation.ts b/packages/angular/build/src/tools/angular/compilation/parallel-compilation.ts
index 6e4debf62501..60945a758081 100644
--- a/packages/angular/build/src/tools/angular/compilation/parallel-compilation.ts
+++ b/packages/angular/build/src/tools/angular/compilation/parallel-compilation.ts
@@ -67,23 +67,28 @@ export class ParallelCompilation extends AngularCompilation {
     );
 
     this.#webWorkerChannel?.port1.close();
+    this.#webWorkerChannel = undefined;
 
-    // The web worker processing is a synchronous operation and uses shared memory combined with
-    // the Atomics API to block execution here until a response is received.
-    const webWorkerChannel = new MessageChannel();
-    this.#webWorkerChannel = webWorkerChannel;
-    const webWorkerSignal = new Int32Array(new SharedArrayBuffer(4));
-    webWorkerChannel.port1.on('message', ({ workerFile, containingFile }) => {
-      try {
-        const workerCodeFile = hostOptions.processWebWorker(workerFile, containingFile);
-        webWorkerChannel.port1.postMessage({ workerCodeFile });
-      } catch (error) {
-        webWorkerChannel.port1.postMessage({ error });
-      } finally {
-        Atomics.store(webWorkerSignal, 0, 1);
-        Atomics.notify(webWorkerSignal, 0);
-      }
-    });
+    let webWorkerSignal: Int32Array | undefined;
+    if (buildType !== 'library') {
+      // The web worker processing is a synchronous operation and uses shared memory combined with
+      // the Atomics API to block execution here until a response is received.
+      const webWorkerChannel = new MessageChannel();
+      this.#webWorkerChannel = webWorkerChannel;
+      const signal = new Int32Array(new SharedArrayBuffer(4));
+      webWorkerSignal = signal;
+      webWorkerChannel.port1.on('message', ({ workerFile, containingFile }) => {
+        try {
+          const workerCodeFile = hostOptions.processWebWorker(workerFile, containingFile);
+          webWorkerChannel.port1.postMessage({ workerCodeFile });
+        } catch (error) {
+          webWorkerChannel.port1.postMessage({ error });
+        } finally {
+          Atomics.store(signal, 0, 1);
+          Atomics.notify(signal, 0);
+        }
+      });
+    }
 
     let success = false;
     try {
@@ -97,12 +102,14 @@ export class ParallelCompilation extends AngularCompilation {
           compilerOptionOverrides,
           buildType,
           stylesheetPort: stylesheetChannel.port2,
-          webWorkerPort: webWorkerChannel.port2,
+          webWorkerPort: this.#webWorkerChannel?.port2,
           webWorkerSignal,
         },
         {
           name: 'initialize',
-          transferList: [stylesheetChannel.port2, webWorkerChannel.port2],
+          transferList: this.#webWorkerChannel
+            ? [stylesheetChannel.port2, this.#webWorkerChannel.port2]
+            : [stylesheetChannel.port2],
         },
       );
       success = true;
diff --git a/packages/angular/build/src/tools/angular/compilation/parallel-compilation_spec.ts b/packages/angular/build/src/tools/angular/compilation/parallel-compilation_spec.ts
new file mode 100644
index 000000000000..7157251e1ab9
--- /dev/null
+++ b/packages/angular/build/src/tools/angular/compilation/parallel-compilation_spec.ts
@@ -0,0 +1,59 @@
+/**
+ * @license
+ * Copyright Google LLC All Rights Reserved.
+ *
+ * Use of this source code is governed by an MIT-style license that can be
+ * found in the LICENSE file at https://angular.dev/license
+ */
+
+import { MessageChannel } from 'node:worker_threads';
+import { AotCompilation } from './aot-compilation';
+import { initialize } from './parallel-worker';
+
+describe('parallel-worker', () => {
+  it('uses incrementing numeric request IDs for transformStylesheet and handles omitted webWorkerPort in library builds', async () => {
+    const receivedRequestIds: unknown[] = [];
+    let workerResult: string | undefined;
+
+    spyOn(AotCompilation.prototype, 'initialize').and.callFake(async (_tsconfig, hostOptions) => {
+      const [style1, style2] = await Promise.all([
+        hostOptions.transformStylesheet('body {}', '/src/a.ts', '/src/a.css', 0, 'CompA'),
+        hostOptions.transformStylesheet('div {}', '/src/b.ts', '/src/b.css', 1, 'CompB'),
+      ]);
+      expect(style1).toBe('transformed:body {}');
+      expect(style2).toBe('transformed:div {}');
+
+      workerResult = hostOptions.processWebWorker('./my.worker', '/src/a.ts');
+
+      return {
+        compilerOptions: {},
+        referencedFiles: ['/src/a.ts'],
+      };
+    });
+
+    const stylesheetChannel = new MessageChannel();
+    stylesheetChannel.port1.on('message', ({ requestId, data }) => {
+      receivedRequestIds.push(requestId);
+      stylesheetChannel.port1.postMessage({
+        requestId,
+        value: `transformed:${data}`,
+      });
+    });
+
+    try {
+      const result = await initialize({
+        jit: false,
+        browserOnlyBuild: false,
+        tsconfig: '/src/tsconfig.lib.json',
+        buildType: 'library',
+        stylesheetPort: stylesheetChannel.port2,
+      });
+
+      expect(receivedRequestIds).toEqual([1, 2]);
+      expect(workerResult).toBe('./my.worker');
+      expect(result.referencedFiles).toEqual(['/src/a.ts']);
+    } finally {
+      stylesheetChannel.port1.close();
+    }
+  });
+});
diff --git a/packages/angular/build/src/tools/angular/compilation/parallel-worker.ts b/packages/angular/build/src/tools/angular/compilation/parallel-worker.ts
index 475592bd478b..dde3df4c0c20 100644
--- a/packages/angular/build/src/tools/angular/compilation/parallel-worker.ts
+++ b/packages/angular/build/src/tools/angular/compilation/parallel-worker.ts
@@ -8,7 +8,6 @@
 
 import type { PartialMessage } from 'esbuild';
 import assert from 'node:assert';
-import { randomUUID } from 'node:crypto';
 import { type MessagePort, receiveMessageOnPort } from 'node:worker_threads';
 import { initializeHash } from '../../../utils/hash';
 import { getAndClearCumulativeDurations } from '../../../utils/profiling';
@@ -29,8 +28,8 @@ export interface InitRequest {
   compilerOptionOverrides?: CompilerOptionOverrides;
   buildType?: 'application' | 'library';
   stylesheetPort: MessagePort;
-  webWorkerPort: MessagePort;
-  webWorkerSignal: Int32Array;
+  webWorkerPort?: MessagePort;
+  webWorkerSignal?: Int32Array;
 }
 
 let compilation: AngularCompilation | undefined;
@@ -52,8 +51,9 @@ export async function initialize(request: InitRequest): Promise<AngularCompilati
       ? new JitCompilation(request.browserOnlyBuild)
       : new AotCompilation(request.browserOnlyBuild);
 
+    let nextRequestId = 0;
     const stylesheetRequests = new Map<
-      string,
+      number,
       [(value: string) => void, (reason: Error) => void]
     >();
     request.stylesheetPort.on('message', ({ requestId, value, error }) => {
@@ -81,7 +81,7 @@ export async function initialize(request: InitRequest): Promise<AngularCompilati
         fileReplacements: request.fileReplacements,
         modifiedFiles: currentModifiedFiles,
         transformStylesheet(data, containingFile, stylesheetFile, order, className) {
-          const requestId = randomUUID();
+          const requestId = ++nextRequestId;
           const resultPromise = new Promise<string>((resolve, reject) =>
             stylesheetRequests.set(requestId, [resolve, reject]),
           );
@@ -98,6 +98,10 @@ export async function initialize(request: InitRequest): Promise<AngularCompilati
           return resultPromise;
         },
         processWebWorker(workerFile, containingFile) {
+          if (!request.webWorkerPort || !request.webWorkerSignal) {
+            return workerFile;
+          }
+
           Atomics.store(request.webWorkerSignal, 0, 0);
           request.webWorkerPort.postMessage({ workerFile, containingFile });