If you have a strong level of assurance that the source of food is halāl, and ingredients used are also halāl, another important factor is the tahārah of the food you eat/drink.
You must make sure there is no cross-contamination with anything najis, whether that be other non-halāl products, or that the person preparing the food is not tāhir.
In the case of when you go to a pizza shop, which might not be exclusively halāl, then there is the problem of cross-contamination. When the toppings are being added in the previous non-halāl order, the person preparing the pizza used tongs or his/her hands for the remaining toppings.
The same is for the knife or roller that cuts the pizza, and it having been used on a non-halāl pizza.
So, the option in this case would be to ask for gloves to be changed, a clean pan to be used, knives to be washed, and toppings to be new.
However, if you have assurance that this isn't the case, and there is no cross-contamination or anything else, then you can consider it tāhir and halāl.
One might argue that such prying into details of food ingredients and matters of halāl and tāhir is too much and is making our lives difficult.
I would say you deal with affairs of your religion and what you eat/drink based on the level of piety and caution you have towards your religion.
And Allah knows best.