Grammargeddon! looked at different style manuals and usage guides and they do not forbid split infinitives:
I’ve looked up “split infinitive” in The Chicago Manual of Style (Chicago, the style guide I use) and on the website for AP, and then I checked Buzzfeed for good measure. After that, I went to the usage guides: Merriam-Webster’s Dictionary of English Usage, Garner’s Modern English Usage, Dreyer’s English (Dreyer), Words into Type, and Fowler’s Dictionary of Modern English Usage.
Not one of these sources says that a split infinitive is to be avoided at all times. In fact, every one of them says that not only is the construction grammatically correct, but it is also preferable to performing syntactical gyrations. There’s no reason to avoid using it when that usage is the clearest and changing it would alter the intended meaning of the sentence.
Furthermore, I’ll note here that the APA style manual, 7th edition, does not even mention split infinitives. As I said to someone in a Slack chat earlier, “APA does not recognize this as a problem.” (Yes, I was being snarky. Imagine that. Thank you to my colleagues DeAnna Burghart and James Fraleigh for being my reference checkers.) Rather, the manual refers users to “a trusted grammar reference” for questions about issues not covered. Which reference? That’s users’ choice.
The only place one might routinely consider avoiding the split infinitive is in the most formal writing, where the most readers are likely to think poorly of its presence (because they’re not grammarians, obviously). Annoying one’s intended audience is seldom if ever the best option.