Nothing is always forbidden in writing. Infinitives are not atoms or hairs or follicle ends. But you ought to know the general rule, so you can decide when to violate it.
An infinitive is the to-plus-action form of a verb, such as to be or not to be, to sing or to dance. In formal prose, a writer should avoid inserting a word between the to and the be, or the to and the dance. The idea was carried over from Latin, where they can’t be split. Simple enough – you write Alice hoped to win quickly, but not Alice hoped to quickly win.
The problem is that adverbs are not very particular as to where they fall in a sentence. They can bounce freely around the syntax. You can add the adverb sometimes to the sentence, Max likes to sleep, almost anywhere you like.
So which of the two rules carries the day?
In speech, the freedom of the adverb wins, especially if there’s any doubt about which verb in a sentence it’s modifying. A speaker might say Mary planned to silently murder John, rather than Mary planned silently to murder John, if a listener couldn’t be sure whether the adverb silently refers to the first verb planned or the second one to murder. Is she planning silently or planning to make the murder silent? Better would probably be either Silently Mary planned to murder John, or Mary planned to murder John silently, depending on how she did what she did.
In formal prose the preference for the united infinitive can create awkward sentences, with the adverb placed awkwardly beforehand to modify a verb that is followed by an embedded sentence, like this one. Break them up to find another way around.
Modern stories rarely require formal prose. We don’t see a lot of colons or semi-colons -- instead, dashes connect independent clauses. In dialogue or interior monologue commas link complete thoughts, suggesting the speed with which words jumble together and thought follows thought.
In a similar way, splitting an infinitive is always a choice when you want to evoke the sound of a voice or maintain the rhythm of a line. Gene Roddenberry did pretty well with the lines, “to seek out new life and new civilizations … to boldly go where no man has gone before.”
Anybody mind that boldly?