Why alternating can be easier at first
Starting on separate nights reduces variables. If redness or stinging develops, you have a better chance of knowing which product or frequency caused it. Once both are stable, the schedule can be adjusted for convenience.
Morning and evening is another simple split
Some people use azelaic acid earlier in the day and retinol at night. That keeps the evening routine shorter and may reduce layering. Sunscreen still matters during the day, especially if uneven tone or post-acne marks are part of the goal.
Product form matters
Azelaic acid comes in cosmetic and prescription products, and textures vary from gels to creams and suspensions. A gritty or occlusive formula may layer very differently from a thin serum. Follow the directions for the products you actually own rather than a generic online order-of-operations rule.
If irritation keeps building
Separate the products again, reduce frequency, and simplify the rest of the routine. Persistent or severe symptoms, or acne that is scarring or difficult to control, are good reasons to involve a dermatologist.