[Nexus 7 Android Development] AndDiSa:
Well, still I do not know what's going on on your tablet, but iny m opinion it has nothing to do directly with Youtube but with fdroid. If you have a look at your logcat, you can see the following part:

11-26 23:06:17.320 I/ActivityManager(738): Start proc 6346:org.fdroid.fdroid/u0a58 for service org.fdroid.fdroid/.data.InstalledAppProviderService
11-26 23:06:17.527 W/ActivityManager(738): Slow operation: 74ms so far, now at attachApplicationLocked: after mServices.attachApplicationLocked
11-26 23:06:19.171 W/System (6346): ClassLoader referenced unknown path: /system/app/FDroid/lib/arm
11-26 23:06:19.462 D/libEGL (6346): loaded /vendor/lib/egl/libEGL_tegra.so
11-26 23:06:19.723 D/libEGL (6346): loaded /vendor/lib/egl/libGLESv1_CM_tegra.so
11-26 23:06:20.137 D/libEGL (6346): loaded /vendor/lib/egl/libGLESv2_tegra.so
11-26 23:06:21.126 I/ACRA (6346): ACRA is enabled for org.fdroid.fdroid, initializing...
11-26 23:06:21.293 I/art (6346): Rejecting re-init on previously-failed class java.lang.Class<android.support.v4.app.JobIntentService$JobServiceEngineImpl>: java.lang.NoClassDefFoundError: Failed resolution of: Landroid/app/job/JobServiceEngine;
11-26 23:06:21.293 I/art (6346): at void org.fdroid.fdroid.data.InstalledAppProviderService.compareToPackageManager(android.content.Context) (InstalledAppProviderService.java:-1)
11-26 23:06:21.293 I/art (6346): at void org.fdroid.fdroid.FDroidApp.onCreate() (FDroidApp.java:374)
11-26 23:06:21.293 I/art (6346): at void android.app.Instrumentation.callApplicationOnCreate(android.app.Application) (Instrumentation.java:1024)
11-26 23:06:21.293 I/art (6346): at void android.app.ActivityThread.handleBindApplication(android.app.ActivityThread$AppBindData) (ActivityThread.java:5406)
11-26 23:06:21.293 I/art (6346): at void android.app.ActivityThread.-wrap2(android.app.ActivityThread, android.app.ActivityThread$AppBindData) (ActivityThread.java:-1)
11-26 23:06:21.293 I/art (6346): at void android.app.ActivityThread$H.handleMessage(android.os.Message) (ActivityThread.java:1547)
11-26 23:06:21.293 I/art (6346): at void android.os.Handler.dispatchMessage(android.os.Message) (Handler.java:102)
11-26 23:06:21.294 I/art (6346): at void android.os.Looper.loop() (Looper.java:154)
11-26 23:06:21.294 I/art (6346): at void android.app.ActivityThread.main(java.lang.String[]) (ActivityThread.java:6122)
11-26 23:06:21.294 I/art (6346): at java.lang.Object java.lang.reflect.Method.invoke!(java.lang.Object, java.lang.Object[]) (Method.java:-2)
11-26 23:06:21.294 I/art (6346): at void com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run() (ZygoteInit.java:889)
11-26 23:06:21.294 I/art (6346): at void com.android.internal.os.ZygoteInit.main(java.lang.String[]) (ZygoteInit.java:779)
11-26 23:06:21.294 I/art (6346): Caused by: java.lang.ClassNotFoundException: Didn't find class "android.app.job.JobServiceEngine" on path: DexPathList[[zip file "/system/app/FDroid/FDroid.apk"],nativeLibraryDirectories=[/system/app/FDroid/lib/arm, /system/lib, /vendor/lib, /system/lib, /vendor/lib]]
11-26 23:06:21.294 I/art (6346): at java.lang.Class dalvik.system.BaseDexClassLoader.findClass(java.lang.String) (BaseDexClassLoader.java:56)
11-26 23:06:21.294 I/art (6346): at java.lang.Class java.lang.ClassLoader.loadClass(java.lang.String, boolean) (ClassLoader.java:380)
11-26 23:06:21.294 I/art (6346): at java.lang.Class java.lang.ClassLoader.loadClass(java.lang.String) (ClassLoader.java:312)
11-26 23:06:21.294 I/art (6346): at void org.fdroid.fdroid.data.InstalledAppProviderService.compareToPackageManager(android.content.Context) (InstalledAppProviderService.java:-1)
11-26 23:06:21.294 I/art (6346): at void org.fdroid.fdroid.FDroidApp.onCreate() (FDroidApp.java:374)
11-26 23:06:21.294 I/art (6346): at void android.app.Instrumentation.callApplicationOnCreate(android.app.Application) (Instrumentation.java:1024)
11-26 23:06:21.294 I/art (6346): at void android.app.ActivityThread.handleBindApplication(android.app.ActivityThread$AppBindData) (ActivityThread.java:5406)
11-26 23:06:21.294 I/art (6346): at void android.app.ActivityThread.-wrap2(android.app.ActivityThread, android.app.ActivityThread$AppBindData) (ActivityThread.java:-1)
11-26 23:06:21.294 I/art (6346): at void android.app.ActivityThread$H.handleMessage(android.os.Message) (ActivityThread.java:1547)
11-26 23:06:21.294 I/art (6346): at void android.os.Handler.dispatchMessage(android.os.Message) (Handler.java:102)
11-26 23:06:21.294 I/art (6346): at void android.os.Looper.loop() (Looper.java:154)
11-26 23:06:21.294 I/art (6346): at void android.app.ActivityThread.main(java.lang.String[]) (ActivityThread.java:6122)
11-26 23:06:21.294 I/art (6346): at java.lang.Object java.lang.reflect.Method.invoke!(java.lang.Object, java.lang.Object[]) (Method.java:-2)
11-26 23:06:21.294 I/art (6346): at void com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run() (ZygoteInit.java:889)
11-26 23:06:21.294 I/art (6346): at void com.android.internal.os.ZygoteInit.main(java.lang.String[]) (ZygoteInit.java:779)
11-26 23:06:21.294 I/art (6346):
11-26 23:06:21.325 I/InstalledAppProvider(6346): selectNotSystemSignature: systemSignature == null, querying for it
11-26 23:06:21.447 I/InstalledAppProvider(6346): excluding InstalledApps signed by system signatures
11-26 23:06:21.818 D/BluetoothManagerService(738): Message: 20
11-26 23:06:22.572 W/art (6346): Suspending all threads took: 25.830ms
11-26 23:06:23.282 I/ActivityManager(738): Process org.fdroid.fdroid (pid 6346) has died
11-26 23:06:23.282 D/ActivityManager(738): cleanUpApplicationRecord -- 6346
11-26 23:06:23.283 W/ActivityManager(738): Scheduling restart of crashed service org.fdroid.fdroid/.data.InstalledAppProviderService in 11630ms
11-26 23:06:34.945 I/ActivityManager(738): Start proc 6382:org.fdroid.fdroid/u0a58 for service org.fdroid.fdroid/.data.InstalledAppProviderService
...

then round about 50 entries like

11-26 23:07:43.837 W/ActivityManager(738): Canceling start item Intent { act=org.fdroid.fdroid.data.action.INSERT dat=package:pl.solidexplorer2 cmp=org.fdroid.fdroid/.data.InstalledAppProviderService (has extras) } in service ComponentInfo{org.fdroid.fdroid/org.fdroid.fdroid.data.InstalledAppProviderService}
...

and then the same thing is starting over with a new org.fdroid.fdroid/.data.InstalledAppProviderService process.

In addition I saw a huge number of messages like

11-26 23:08:22.633 E/sdcard (1695): *** NOTIFY FAILED *** 22

I would do the following:

1. do an fsck of your file system on /data and /cache

2. re-install fdroid ?!

I never used fdroid, so I cannot say how to solve that issue. Probably there are also some permissions for fdroid missing ... here you are on your own.