Should I not invite my husband's unvacqinated brother in law?

My birthday is coming up soon and I really want to have a birthday party at our new home. We bought it during the pandemic so we have not had any gatherings at the house yet. During the pandemic we did not see any of our friends or a cousin of mine and his family that live in town. My husband has a stepsister in town and we did see her and her family a few times during the pandemic. My husband and I are fully vaccinated and we have a 3.5 year old who obviously cannot be vaccinated so we decided to make sure we only interacted with vaccinated people. The only problem is that my sister-in-law' husband has not been vaccinated because he says he faints when he sees needles and has been putting it off. We just started seeing our friends that have been vaccinated and only because they were vaccinated. Should I not invite him? I feel like it isn't fair to other guests who do not want to interact with unvacinated people. Should I ask him to wear a mask?