What is the ruling on working in a grocery store that sells food and beer in Western countries, knowing that beer is a light type different from wine, and is it permissible to perform Hajj with this money if my mother and I intend to do Hajj?

If beer is mixed with alcohol such that consuming a little or a lot of it intoxicates, then it is not permissible to consume or sell it, because it is considered khamr (intoxicant).

If it is possible to avoid selling beer at work, then remaining there is not unlawful. However, if you are compelled to sell it, then it is not permissible to remain except in cases of extreme necessity.

The money earned from this work is not entirely unlawful. Rather, the unlawful portion is commensurate with the work involved in the prohibited sales, and this portion must be disposed of. What remains is lawful and can be used for Hajj.

It is not permissible to remain in lands of disbelief except for one who is safe from temptation and can uphold the rituals of their religion. A woman should seek work that suits her femininity and adheres to Islamic guidelines.