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

Yes

The word "misturar" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The primary difference is pronunciation: Brazilian Portuguese tends to have more open, phonetic vowels, whereas Continental Portuguese features more closed, reduced vowels and a different rhythmic stress. While the word itself does not change, the way a speaker addresses someone (using você in Brazil vs. tu in Portugal) will change the conjugation of the verb in a sentence, though the verb "misturar" remains the same.

Brazilian Portuguese Examples

1. Eu vou misturar os ingredientes agora. (I am going to mix the ingredients now.)
2. Você não deve misturar as roupas brancas com as coloridas. (You should not mix the white clothes with the colored ones.)
3. Ela gosta de misturar música pop com ritmos brasileiros. (She likes to mix pop music with Brazilian rhythms.)
4. É fácil misturar as tintas para chegar ao tom certo. (It is easy to mix the paints to reach the right shade.)
5. Não se misture com pessoas que não te fazem bem. (Don't mix/associate with people who are not good for you.)

Continental Portuguese Examples

1. Eu vou misturar os ingredientes agora. (I am going to mix the ingredients now.)
2. Não deves misturar a roupa branca com a colorida. (You should not mix the white clothes with the colored ones.)
3. Ela gosta de misturar música pop com ritmos brasileiros. (She likes to mix pop music with Brazilian rhythms.)
4. É fácil misturar as tintas para chegar ao tom certo. (It is easy to mix the paints to reach the right shade.)
5. Não te mistures com pessoas que não te fazem bem. (Don't mix/associate with people who are not good for you.)