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

Yes

The spelling, meaning, and grammatical function of the word "religião" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• Brazilian Portuguese: The "i" is typically pronounced with a clear, palatalized "ee" sound, and the nasal diphthong "ão" is more open and resonant.
• Continental Portuguese: The "i" is often more reduced or "shortened," and the "ão" is pronounced with a more closed and heavily nasalized sound.

Brazilian Portuguese Examples

1. Eu respeito a religião de todo mundo. (I respect everyone's religion.)
2. Qual é a sua religião? (What is your religion?)
3. A religião é muito importante na minha vida. (Religion is very important in my life.)
4. Ele gosta de estudar várias religiões. (He likes to study various religions.)
5. A gente não deve misturar religião com política. (We shouldn't mix religion with politics.)

Portuguese (Portugal) Examples

1. Eu respeito a religião de todos. (I respect everyone's religion.)
2. Qual é a tua religião? (What is your religion?)
3. A religião é fundamental na minha vida. (Religion is fundamental in my life.)
4. Ele estuda as diversas religiões do mundo. (He studies the diverse religions of the world.)
5. Não se deve misturar religião com política. (One should not mix religion with politics.)