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

Yes

The word "religiosa" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference lies in pronunciation and the phonetic rhythm of the sentence:

• Pronunciation: In Brazilian Portuguese, the vowels are more open and clearly articulated, and the word has a more "musical" or melodic quality due to a syllable-timed rhythm. In Continental Portuguese, unstressed vowels (like the "i" in the middle of the word) are often "reduced" or swallowed, making the word sound more "clipped" and consonant-heavy.
• Syntax: While the word itself does not change, the way a Portuguese person would structure a sentence around it often differs, particularly regarding the placement of object pronouns (clitics).

Brazilian Portuguese Examples

1. Ela é uma mulher muito religiosa. (She is a very religious woman.)
2. A música religiosa acalma o coração. (Religious music calms the heart.)
3. Ela faz parte de uma organização religiosa. (She is part of a religious organization.)
4. A educação religiosa é ensinada na escola. (Religious education is taught in school.)
5. Ela se dedica à vida religiosa. (She dedicates herself to religious life.)

Continental Portuguese Examples

1. Ela é uma mulher muito religiosa. (She is a very religious woman.)
2. A música religiosa acalma o coração. (Religious music calms the heart.)
3. Ela faz parte de uma organização religiosa. (She is part of a religious organization.)
4. A educação religiosa é ensinada na escola. (Religious education is taught in school.)
5. Ela dedica-se à vida religiosa. (She dedicates herself to religious life.)