Should you always start a new paragraph when starting a new speaker even if the sentence directly before that is directly related?

When a new speaker starts a new line of dialogue you start a new paragraph at the same time. Does this rule still hold true if the sentence before the dialogue starts relates directly to the dialogue?

For example, can you write:

Simon stared at her.
"Are you serious?"

like this:

Simon stared at her. "Are you serious?"

instead?

Is this a simply style choice or an error?

I believe the conventional rule is that you start a new paragraph when the speaker changes, not when any quote starts. You may have other text before the quote, as long as it's not a quote from a different speaker. You may or may not start a new paragraph when a quote follows non-quote text. Indeed we routinely precede quotes with text identifying the speaker, like "John replied" or "Mary paused for a moment before speaking."

So by the conventional rules:

Simon stared at her. "Are you serious?"

"I certainly am," Mary replied.

Do not normally run multiple speakers into one paragraph:

Simon stared at her. "Are you serious?" "I certainly am," Mary replied.

This rule can be counterproductive when you have two or more short quotes within a block of narrative. I sometimes ignore it in such cases, but I'm sure an English teacher would mark it wrong. Like:

We had a long discussion about which way to go. John said, "Let's head north." But others in the group where not sure this was a good idea. We argued for a long time. Finally Alice said, "Okay, let's go north."

I'd prefer to write it like I did above, one long paragraph, but purists would say that "Finally" should begin a new paragraph.

It is a style choice. However, I would say that the first example with the new paragraph is stylistically inferior, because it dissociates the speech from the speaker; with the break, the expectation is that someone new has started talking. If the two actions (the staring and the talking) are connected, then putting in the paragraph break causes the reader to have to stop and re-evaluate who's saying it, distracting from the flow. I think you want to either write it as

Simon stared at her. "Are you serious?"

where the actions are implicitly connected to the same actor, or

Simon stared at her.

"Are you serious?" he asked.

where they are explicitly connected.