When you say are they thread safe, presumably you mean can you use them in multiple threads without having to lock anything.
In theory you could potentially have 2 threads, one pushing to the back and one to the front, and you'd probably get away with it although I would be wary because the implementor is not under a guarantee to make it thread safe as iterators become invalidated with inserts at either end, if the implementation of push_back used "end" and of push_front used "begin", such would be invalidated in the call by the other thread, and might blow up on you.
std::priority_queue is almost certainly not usable in two threads together, presumably for producer/consumer threads, with one pushing and one popping and you will need to lock first.
I found that when I wrote a producer/consumer queue based around std::deque, I allowed the producer also to push more than one item at a time, and the consumer to sweep the entire queue to process. This meant only one lock per bulk-insert, so reduced the number of times you needed to lock.