Do you mean people making posts that have news links in them, or people boosting posts from news accounts?
If it's boosts, you can hide people's boosts without blocking them completely (more info: https://fedi.tips/blocking-and-muting-on-the-fediverse/#JustBoosts ).
First thing to do is check their profile to see if they have any preferences about being contacted (or not contacted).
If they have a link to a personal website in the profile, it's worth clicking on that and seeing if it has a contact page.
If there's nothing about this in their profiles and they don't have a contact page, you can try sending a private message by using the mention-only post.
In general, however active your account is, if there's someone impersonating you, report it to your own server admin and to the admin of the server where the impersonator is. If the remote server refuses to take action, your own admin may choose to restrict or block the remote server.
You can hide your account's follow and follower lists to prevent anyone copying them (more info: https://fedi.tips/how-to-hide-your-follows-and-followers-in-mastodon ).
Deletion would make it harder to prove you're being impersonated or cloned.