How would you usually deal or cope with the idea if J was interested in seeing someone that was single and not familiar with the open concept, but wanting to know more? I'm having a difficult time relaxing about it, so I thought maybe hearing someone else's perspective on it might help a bit.
I think this is a pretty common sentiment. Many people I know in open relationships, myself included, feel threatened thinking about their partner dating someone who may be monogamously oriented and not respect my relationship with J.
I think, too, the idea of J dating single people was initially more threatening for me, because those single people don't have other partners taking up time and commitment, and so may demand more time and commitment from J. There wasn't a sort of predetermined "cap" on where the relationship "could go" because other relationships took up time and energy in that person's life. (I am aware these feelings reflect couple privilege, and a bias toward considering romantic relationships versus familial ones or friendships. These have been feelings of mine, and not my logical conclusions around this issue.)
However, I think it is really important to figure out what exactly you feel threatened by and communicating this to your partner. You can then either ask for something (a behavior change, reassurance, etc.) or simply trust that by expressing your concerns to your partner, they will be sensitive to your feelings.
Also, it is important to try to remember that each person is different. This new person may end up deciding that they don't want to operate in an open relationship. The new person may end up deciding they absolutely love open relationships and want more from your partner, happy with how much they have, or are ready to move on from your partner. The person may be someone you get along with really well or someone that you don't. They may convey a lot of respect toward you and your relationship or disinterest or disdain. So many situations and dynamics are possible, and you simply can't account for all of them. And you can drive yourself crazy trying to prepare for everything, when it simply isn't possible.
I think being open as you can toward the unknown can help. What do you know? You know yourself, and you know as much as you can about your partner. You know your work, where you live, what you stand by. Remain in your core to stay open and compassionate.
Practically, figure out strategies that may help alleviate your anxiety: Ask your partner about basic information about the person. Ask to meet the new dating partner. These things may help you get evidence for yourself that the new partner is someone you can basically trust to respect you and your relationship.
Also: role model what being in an open relationship is all about. This person is new to the world of open relationships? Show them how it's done! With clear, transparent, and compassionate communication, integrity, and an open heart. By showing yourself, your partner, and the new partner who you are and how you operate, how can you not elicit some level or respect? :)