Learn Hardcore Spanish (Latin America): Mi nutricionista dice que la dieta debe ser moderada. - My nutritionist says that the diet must be moderate.

Mi means my, so mi nutricionista is my nutritionist.
If you said el nutricionista, that would be the nutritionist, referring to some nutritionist in general, or one that is known from context, but not clearly yours.

All are possible, but they mean different things:

Mi nutricionista = my (personal) nutritionist
El/la nutricionista = the nutritionist (the one we both know about)

Can nutricionista be masculine or feminine? How do I say “my male/female nutritionist”?

Yes, nutricionista can be masculine or feminine; the ending -ista doesn’t change.
You show the gender with the article (or other words around it), not with the noun itself:

El nutricionista = the male nutritionist
La nutricionista = the female nutritionist
Mi nutricionista could be either; context would tell you.

So the sentence doesn’t specify if the nutritionist is a man or a woman.

Why isn’t there a subject pronoun like él or ella before dice?

Spanish normally drops subject pronouns when the verb ending already shows who the subject is.
Dice is the 3rd person singular form of decir (to say), so it already implies he/she/it says.

You could say Él dice que… or Ella dice que…, but you only do that when:

you need to clarify who you’re talking about, or
you want to emphasize he or she.

In neutral, normal speech, Mi nutricionista dice que… is more natural.

What does dice que literally mean, and do I always need the que?

Dice que literally means (he/she) says that.
Here, que is a conjunction introducing a subordinate clause: que la dieta debe ser moderada = that the diet must be moderate.

Unlike English, you cannot drop the que here.
In English you can say “My nutritionist says (that) the diet must be moderate”.
In Spanish you must say Mi nutricionista dice que la dieta debe ser moderada — leaving out que is ungrammatical.

Why is it la dieta and not just dieta or una dieta?

La dieta means the diet, referring to a specific diet that both speaker and listener can identify (usually the person’s current diet or the plan they are following).

Alternatives would slightly change the meaning:

Mi dieta = my diet (focusing on my personal diet)
Una dieta = a diet (any diet, not a specific one)

Spanish also uses definite articles more often than English, especially when talking about things in a general or habitual way, so la dieta sounds very natural.

Why is debe used here? What’s the difference between debe, tiene que, and debería?

All three express obligation or recommendation, but with different strength and nuance:

debe ser moderada ≈ must / should be moderate
Neutral obligation or strong recommendation. Often used in formal or professional advice.
tiene que ser moderada ≈ has to be moderate
Sounds a bit more like a requirement or necessity, more colloquial/stronger in everyday speech.
debería ser moderada ≈ should be moderate
Softer and more hypothetical; it’s advisable, but sounds less strict.

Here, debe fits a professional giving clear advice or guidelines.

Why is ser used instead of estar in debe ser moderada?

Ser is used for more permanent characteristics, definitions, or inherent qualities.
Estar is used for temporary states or conditions.

A dieta moderada is being described in terms of what it should be like in general (its overall character), not a temporary condition.
So you say:

La dieta debe ser moderada. = The diet must be moderate (as a general principle).

If you used estar, it would sound like you’re talking about a temporary state, which doesn’t fit well with the idea of a diet’s overall nature.

Why is moderada feminine? Does it have to agree with dieta?

Yes, adjectives in Spanish must agree in gender and number with the noun they describe.

dieta is a feminine singular noun.
So the adjective must also be feminine singular: moderada.

Compare:

El plan debe ser moderado. (masculine singular: plan → moderado)
Las dietas deben ser moderadas. (feminine plural: dietas → moderadas)

Moderado (with -o) would be wrong here because it doesn’t match la dieta.

Can I put the adjective before the noun, like la moderada dieta?

Grammatically, yes, you can say la moderada dieta, but it sounds literary or poetic, not like normal everyday speech.

In standard, neutral Spanish, descriptive adjectives usually come after the noun:

la dieta moderada (normal)

Adjectives before the noun are used for style, emphasis, or certain fixed expressions. So in this sentence, la dieta debe ser moderada is the natural, everyday word order.

Why isn’t the subjunctive used after dice que? Could it be Mi nutricionista dice que la dieta deba ser moderada?

With decir que, Spanish uses:

the indicative when reporting information or opinions, and
the subjunctive when expressing a command or wish directed at someone.

In your sentence, the nutritionist is stating a fact/opinion about the diet, so Spanish uses the indicative:
la dieta debe ser moderada (not deba ser).

But compare:

Mi nutricionista me dice que coma menos azúcar.
= My nutritionist tells me to eat less sugar.
Here, coma is subjunctive because it’s a command directed at me, not a reported fact.

So Mi nutricionista dice que la dieta debe ser moderada is correct and natural; …deba ser moderada sounds unnatural in this context.

Is nutricionista the most common word in Latin America, or would people say something else?

In most of the Spanish-speaking world, nutricionista is widely understood and common.
However, in much of Latin America (especially Mexico and some Central American countries), you’ll also hear nutriólogo / nutrióloga for a nutrition specialist.

So in many places, you could also say:

Mi nutriólogo dice que la dieta debe ser moderada. (male)
Mi nutrióloga dice que la dieta debe ser moderada. (female)

Both nutricionista and nutriólogo/a are correct; usage depends on the country and local preference.