Step 1: The microscopy clue is decisive: budding yeasts with pseudohyphae are the diagnostic features of Candida albicans. The oral white mucosal patches in an HIV patient are oral candidiasis (thrush).
Step 2: Candidiasis is the most common opportunistic oral infection in HIV. The white plaques can be scraped off, leaving a raw erythematous base, which separates it from the other options.
Step 3: Why the others are wrong. Hairy leukoplakia is caused by Epstein-Barr virus, appears on the lateral tongue, cannot be scraped off and shows no yeasts. Lichen planus shows Wickham striae and a band-like lymphocytic infiltrate, not yeasts. Diphtheria produces a grey pharyngeal pseudomembrane from Corynebacterium diphtheriae, not budding yeasts.
Ref: Robbins Basic Pathology, pg 502-503.