Is the word abacate the same in Brazilian and European Portuguese?

Yes

The word "abacate" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• Brazilian Portuguese: The vowels tend to be more "open" and pronounced. The unstressed "e" at the end of the word is typically pronounced as an "i" (/abáka-tʃi/).
• Continental Portuguese: The vowels are more "closed" or reduced. The unstressed "e" at the end of the word is often neutralized or pronounced as a very short, nearly silent sound (/abáka-t/).

Brazilian Portuguese Examples

1. Eu adoro comer abacate no café da manhã. (I love eating avocado for breakfast.)
2. O abacate está muito maduro hoje. (The avocado is very ripe today.)
3. Você prefere suco de abacate ou vitamina? (Do you prefer avocado juice or a smoothie?)
4. Fiz uma torrada com abacate e ovo. (I made avocado toast and egg.)
5. Preciso comprar um abacate na feira. (I need to buy an avocado at the street market.)

Continental Portuguese Examples

1. Eu adoro comer abacate ao pequeno-almoço. (I love eating avocado for breakfast.)
2. O abacate está muito maduro hoje. (The avocado is very ripe today.)
3. Preferes sumo de abacate ou batido? (Do you prefer avocado juice or a smoothie?)
4. Fiz uma torrada com abacate e ovo. (I made avocado toast and egg.)
5. Preciso comprar um abacate no supermercado. (I need to buy an avocado at the supermarket.)