With Facebook Messenger, you now have the option to hide the "Active" status. So the time you were online would be displayed in the Active ago… field and will not change even if you continue to use Messenger.
Steps
Method 1 of 2: Hide the "Active" status with a phone

Step 1. Open the Messenger app
It looks like a blue bubble around a white lightning bolt.
- If you haven't signed in yet, enter your phone number. Then press To continue then enter your password.

Step 2. Tap People
You can find this button at the bottom right of your screen.

Step 3. Press the ONLINE tab
This button is near MESSENGER. You can find it at the top of your screen, just below the search bar.

Step 4. Press the switch
Press the switch in front of your username to toggle it to “off” (left). After this action, it will turn gray and the list of your active contacts will disappear. While receiving messages, your profile will appear offline and the timestamp next to your name will display the time you logged out.
Method 2 of 2: Hide "Active" status with desktop version of Facebook

Step 1. Visit the Facebook home page
You should be redirected to your news feed.
- If you are not yet signed in, enter either your email address or your phone number and password. Then select Log in by clicking on it. You will see this option in the upper right corner of your screen.

Step 2. Click ⚙️
This icon is located at the bottom right of the page.

Step 3. Click on Disable Instant Chat
You will find this option in the drop-down menu that appears.

Step 4. Click on Disable Chat for All Contacts
This will allow you to prevent your contacts from seeing your name in the category. Active.
- You also have the possibility to click on the option Disable chat for all contacts except …. To do this, you must first click on advanced settings. The option Disable chat for all contacts except …, will allow you to select the contacts for which you want to stay online. In addition, you can click Disable chat for just a few contacts … to select specific contacts for which you want to appear offline.

Step 5. Click Save
Your chat bar will turn gray and you will appear offline to all contacts who search for your name in their chat bar. The timestamp next to your name will show the time you logged out. Even if you continue to use Messenger, this time will not change.
Advice
- If you are using Messenger on the desktop version of Facebook, click Settings, then on Active contacts and finally on the switch in front of your profile name to go offline.