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

Yes

The fundamental meaning, spelling, and grammar of the word "abrigo" are identical in both Brazilian and Continental Portuguese. It refers to a place of protection, a refuge, or a shelter from the elements. While the word can occasionally refer to a set of athletic clothing (a tracksuit) in both dialects, the primary difference between the two variants is pronunciation. Brazilian Portuguese tends to pronounce vowels more openly and clearly, whereas Continental Portuguese features significant vowel reduction, often making unstressed vowels sound shorter or nearly swallowed.

Brazilian Portuguese Examples

1. Precisamos encontrar um abrigo para fugir da chuva. (We need to find shelter to escape the rain.)
2. O abrigo de animais recebeu muitas doações hoje. (The animal shelter received many donations today.)
3. Eu gosto de usar esse conjunto de abrigo quando está frio. (I like to wear this tracksuit when it is cold.)
4. O governo construiu um novo abrigo para os desabrigados. (The government built a new shelter for the homeless.)
5. Eles buscaram abrigo na caverna durante a tempestade. (They sought shelter in the cave during the storm.)

Continental Portuguese Examples

1. Precisamos de encontrar um abrigo para nos protegermos da chuva. (We need to find shelter to protect ourselves from the rain.)
2. O abrigo de animais recebeu muitos donativos hoje. (The animal shelter received many donations today.)
3. Eu gosto de usar este fato de treino quando está frio. (I like to wear this tracksuit when it is cold.)
4. O governo construiu um novo abrigo para os sem-abrigo. (The government built a new shelter for the homeless.)
5. Eles procuraram abrigo na gruta durante a tempestade. (They sought shelter in the cave during the storm.)