No, you do not have to worry about new popcorn ceilings having asbestos. All residential building materials used since the mid-1980s stopped including asbestos, so new popcorn ceilings have no risk of asbestos. You can still create a textured drywall ceiling with a popcorn texture if you like, but new techniques have no risk of adding asbestos. 

Asbestos has many beneficial properties, including fire resistance, strength, and chemical resistance. It is also an excellent insulator, which is why it was used in pipe insulation and other building materials for decades. For all its benefits, asbestos is dangerous for human health, which is why it was eventually banned from use in certain products.

Since the EPA partially banned asbestos in 1989, it is no longer used to manufacture new siding in the United States; production had largely ceased by the early 1980s. Many other countries, such as Canada, Iceland, and Denmark, also have bans on asbestos. However, asbestos siding is still present in many homes built before the late 1980s. The only definitive way to know if your siding contains asbestos is to have it professionally lab-tested.

It is not recommended to drill into asbestos siding because doing so can release hazardous asbestos fibers into the air. The safest way to handle asbestos-containing materials is to have a professional remove or encapsulate them.