Is it possible to have giardia and pinworms at the same time?

Yes: Both are spread by fecal-oral route. Pinworms are usually asymptomatic except for anal itching, but Giardia can cause persistent diarrhea illness. If both are present, I recommend Rx for both

Yes: Yes, they can be contracted in the same types of environments.

Giardia: Threadworms are small, thin, white, thread-like worms between 2 mm and 13 mm long. They infect human guts (intestines). They are common in children, but anyone of any age can be affected . Giardia intestinalis - also known as Giardia lamblia or - is a living thing that lives in, or on, another living organism . It can infect your bowels and cause giardiasis

Yes: There is nothing to prevent simultaneous Giardia and pinworm infections.