I was able to read at least part of the article without a subscription. Folks wanted to send Nixon some pointed complaints (go figure, who could have imagined) and telegraph operators weren’t letting them. Seems telegraph companies left matters of decency up to the discretion of the operator, at least by 1970 (and I bet you’d get a lot of “you may take your business elsewhere” for various sorts of messages you tried to send, before that, to the point that much speech was de-facto banned)
Have you ever had your TV get disabled because your cable company didn't like the content you were watching?
140 years ago in the age of telegram, I suspect they weren't censoring messages they didn't like either.