Is there a way to turn this off? I don't want to see whether my contacts are 'active now.'
No there is no direct way to do so. Alternatively you can turn off chat on messenger then you will not see 'Active Now' status of your contacts.
Note: When you turn chat off, you'll still get your messages, but people won't see a green small circle (online symbol) next to your name, and you won't appear in the Active tab.
You can actually hide it. You have to do it from the messenger app on your phone. You will open messenger and it should pop up and show a list on conversations but at the very top there are 4 options you can click on. You'll click on the 3rd one over. It's like 3 bullet points with lines beside it. Once you click on that you will see something that says messenger and active. Click on the Active tab. There is a little on/off switch beside your name. Slide it to off. And now people can't see if you are online or when you were last online.