Can you max every Confidant in one playthrough?
Yes — Royal gives you enough evenings to do it on a first run, but only if you unlock Chihaya (Fortune) early and start every Confidant as soon as it appears.
It's possible without New Game Plus, and the two decisions that make or break it are both made before summer.
Yes. Unlike the original Persona 5, Royal gives you enough time to max every Confidant on a first playthrough — no New Game Plus required. It is not, however, something that happens by accident, and by August it can already be out of reach.
Two things do most of the work.
Chihaya, the Fortune Confidant, is the whole trick. Her fortune-telling lets you buy a relationship forward: 5,000 yen adds two points to a Confidant's progress — three if you're carrying a Persona of their Arcana. That's an evening you didn't have to spend, bought with money you have plenty of. Unlock her as early as the game allows and the maths stops being tight.
Start every Confidant the day it becomes available. The failure case is almost never «I ran out of days at the end», it's «I started four people in November». A Confidant you meet in April and see once a fortnight finishes comfortably; the same person begun in October cannot.
Royal also quietly hands you more evenings than the original did — Morgana stops sending you to bed nearly as often — which is the structural reason this is possible now and wasn't before.
The one thing that will still stop you is a social stat check: several Confidants refuse to advance past a certain rank until Knowledge, Charm, Kindness, Guts or Proficiency is high enough. That's why the stats and the school calendar matter more than they look — the class and exam answers are free Knowledge, and how the stats gate people is the other half of this answer.