The most successful partner yoga situation is one in which you can trust your partner to give a safe assist and offer the same back to them. Partner yoga workshops, in which you bring your own partner (ideally a friend who has a complimentary practice), can be a great way to deepen a relationship and a yoga practice simultaneously. The more difficult scenario is when you are assigned to work with a stranger in your yoga class. There are two levels of concern here, one mental and the other physical. On the mental level, many of us feel an aversion to being compelled to engage with another person, especially since that engagement involves touching. However uncomfortable at first, this is actually a good exercise in letting go of our conventional assumptions of what we do and don't like and allowing ourselves to connect with another person. There is a lot of talk about getting your body to open up in yoga, but getting your mind to open up is just as important and often harder to achieve. Challenge yourself to continue attending that class where the teacher loves to call out, "ok, everybody partner up!" and try to work out a way through your discomfort.
The second, very real, concern is for your physical safety. If you are partnered with someone who seems too inexperienced, be very vocal, though polite, in directing them to ease off their adjustment. (Though I have found that, in general, someone who is nervous about giving adjustments tends to be very tentative rather than overly aggressive.) If your partner seems ill-equipped to support or catch you, say, in an inversion, don't be afraid to opt out of that pose or ask the teacher to be a back up. In short, be open, aware, and friendly while taking responsibility for your own safety.