Even if a store claims to be halal, I’ll still look into it…even for Muslim shops. I know people in the meat supply business, so I’ll go with the suppliers or shops that they recommend. So just the halal label or claim doesn’t cut it for me.
In terms of Canadian stores (or rather non-Muslim/non-desi etc), I actually buy some meat items from Walmart would be open to buying it from other supermarkets. I look at the certification (HMA) and then even if someone claims to be certified, I’ll cross check with the HMA (Halal monitoring authority) to ensure that they’re really certified.