Friends, co-workers and relatives are asking each other one tricky question: Are you vaccinated?

As the highly contagious Delta variant of Covid-19 surges, asking about vaccination status has taken on new urgency—and complexity. The question can damage personal and professional relationships if not handled carefully.

“It’s such a simple question, but it’s so fraught,” says Marissa King, a professor of organizational behavior at the Yale School of Management and author of “Social Chemistry: Decoding the Patterns of Human Connection.” People tend to avoid contentious topics in order to preserve networks and relationships, she says. “We don’t know how to have these conversations in a way that can be productive.”

About half of all Americans are fully vaccinated, according to the Centers for Disease Control and Prevention, leaving plenty of room for mixed-status groups at parties, play dates and office meetings. While vaccinated people are far less likely to experience severe illness or death, it is still possible for them to develop infections and potentially transmit the virus to others, including children who aren’t yet eligible for the shots, along with adults who have weakened immune systems.

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So, how to ask about someone’s vaccination status? For the greatest chance of minimizing damage to a relationship, communication advisers recommend staying dispassionate. Try to divorce the query from your political and moral views, no matter how strong, says clinical psychologist Catherine Steiner-Adair.

“Don’t let your brain override your capacity to stay present in a calm way,” she says. She has honed the skill by listening to news channels she doesn’t agree with.

Here’s how communication experts suggest approaching questions about vaccination status in different scenarios: at work, in social situations and with extended family.

AT WORK

When asking a co-worker, it’s helpful to provide a reason for your question. Make clear that you’re not passing judgment but simply trying to learn and problem-solve, says Douglas Stone, co-author of “Difficult Conversations: How to Discuss What Matters Most.”

You won’t violate privacy regulations under HIPAA, the Health Insurance Portability and Accountability Act, by asking about a co-worker’s vaccination status since you’re not their healthcare provider or insurer, and you’re asking about, not disclosing, health information, says Robert Gatter, a law professor at St. Louis University School of Law and Center for Health Law Studies. Even if asking is legal, it’s still awkward, he notes.

Deborah Tannen, linguistics professor at Georgetown University and author of “That’s Not What I Meant! How Conversational Style Makes or Breaks Relationships,” suggests saying something like: “By the way, I know quite a lot of people who aren’t vaccinated and I understand the reasons, but I would appreciate knowing. I’m trying to get a sense of who in the office is vaccinated to know where to have meetings, whether to have people in my office.” Let people know you’re asking everybody, she says, and that the reason for the question is to determine how best to get the work done.

Dr. King suggests letting a co-worker know how the uncertainty affects you personally. Say, for instance: “I respect your choice, but when we don’t wear masks, it makes me feel unsafe and makes it difficult for me to get my work done.” Prepare yourself for an uncomfortable response, she recommends, and practice how you might reply to hostility. She suggests saying, “OK, thanks for letting me know,” and stepping away. “There may be other solutions available if you give more space and time to think about it,” she says.

Stay civil and respectful. You likely need to maintain professional relationships with co-workers regardless of their status, and individual workers don’t have much sway over their environments. “You don’t have control,” Dr. King says.

IN SOCIAL SITUATIONS

You can control who you socialize with, but the vaccination question has the potential to damage relationships as you determine who can and can’t attend a party, come to your house, or play with your kids, says Dr. Tannen.

You may want to soften the question by saying: “I know I’m being overly cautious,” says Dr. Tannen. If you’re concerned about exposing an at-risk family member or elderly parent, explaining your worry may help defuse tension.

SHARE YOUR THOUGHTS

How do you ask people about their vaccination status? Join the conversation below.

Leadership coach Deborah Riegel suggests introducing the question with a mix of vulnerability and humor: “ ‘I need to ask you something really awkward’…or ‘I need to ask you something that feels a little personal, so let me apologize in advance’…‘I promise I’m not going to ask your salary or did you get a face-lift,’ ” she says.

Emphasize that you value the relationship, regardless of the person’s vaccination status. That’s particularly true when it comes to assessing the safety of your children’s play dates.

Dr. Steiner-Adair suggests starting a parent-to-parent conversation with “Pease don’t take this personally,” then acknowledging how much you value the friendship between your kids. (The same can be true of siblings or book-club members.) Explain that “as a family right now, we’ve had to make some difficult decisions.” She counsels to make the issue “little, not big,” starting with “May I have a quick conversation with you?”

WITH FAMILY

Questions about vaccination can stir up power struggles in families. An email invite to a Labor Day cookout can clearly ask that everybody be vaccinated. What to do if a cousin replies that he’s not vaccinated but looks forward to attending? Do you, the host, tell him he can’t come? Or do all other family members need to decide differently?

“There are a lot of dynamics at play. Somebody could really hold the event hostage,” Ms. Riegel says.

Anticipate the different scenarios, make a plan for handling them and know it may not go smoothly. Accept that you may have to make a decision that will hurt someone’s feelings. “You may have to deal with a little bit of discomfort and backlash,” says Ms. Riegel. “Just say, ‘I know everybody’s entitled to their own decisions and I’m not there to judge. I’m just here to make decisions for my family.’ ”

If the conversation goes awry, stop and pause. “If we don’t allow [conversations] to defuse, then repairing that conflict can take far, far longer than just taking the time to pause,” says Dr. King. Ms. Riegel suggests “noticing and naming neutrally” that the conversation has gotten off track with a comment like: “I noticed that we are talking about politics now rather than plans.” Then suggest taking a break and revisit when emotions have cooled.

Write to Betsy Morris at betsy.morris@wsj.com