Of course they do–and this does not just include active congregations. I know many contemplative sisters with library cards. Some use them to check out ebooks, some films, etc. Different monasteries have differing understandings of enclosure. For example, one Carmelite community I know has a rotation of sisters who do grocery shopping and other essential errands, and they go by the public library at the same time.
A library card is also a way of maintaining (not challenging) the vow of poverty.
In New York state, too, any resident of the state can use the NY Public Library (NY City). It is a fantastic resource, and during the pandemic it’s been fantastic to have access to its large collection of ebooks–much larger than in many smaller library systems in the state. Why shouldn’t religious have access to such resources? They are, after all, citizens.