Yes. Normally you can have one thread writing to a data structure OR many threads reading the data structure at any given time and not need to worry about them causing problems. (This situation is common enough that we have things called "reader-writer mutexes" or "shared-exclusive" mutexes.)

As soon as your reads can modify the internal state of the data structure, it might modify the state in a way which trips up another read; so you can no longer have many threads reading the data structure at once.