Poultry in non glatt restaurant

Question

What about where the store and the owners are Shomer Shabat. I saw such a store in NJ, where the owners felt that they needed nonjewish customers to make the restaurant viable economically, and went with Hebrew National as a nationally known brand. Would the ownership being Shomer Shabat change the psak as far as poultry products sold in the store?DW is it ok to eat chicken and turkey at a "kosher" restaurant that serves all kosher foods except for the fact that there meat like hot dogs are hebrew national and not glatt kosher? if so are there any other types of meats along with chicken and turkey that may be eaten there? Thanks!