Partner dancing has nothing to do with affection. Everyone is encouraged to dance with everyone.
No matter your gender, sex, or orientation. Nothing matters except the music and the community!
Social dancing is a great opportunity to meet new and interesting people of course. But, this is NOT a single's club. This is not where people come to hook up, specifically. If you're looking for sex this is the wrong place. But, if you're looking for meaningful connections. If you're looking for a great place to network, and, perhaps meet the love of your life. The Lindy Hop community is what you are looking for.
Have you ever thought you maybe should make some friends? Friends outside of work. Friends outside of school? But, how do we make friends as adults in this world?
Lindy Hop dancing as a casual social activity
Dancing (specifically partner dancing) was, in all probability one of the pastimes of your grandparents, great-grandparents, and so on. But the same attitude that brought your ancestors out dancing with their friends and family in much of US culture has disappeared. (And changed). Partner dance as a casual activity is normal for many other cultures throughout the world, including much of the US. I don't have sources to cite on this claim. But, I would venture to claim that few other cultures who have partner dancing as a regular part of their community gatherings regard what they do as skilled expertise in the same way that much of the US cultures have a divide between "dancers" and "non-dancers".
If you think dancing is silly, if you think dancing is "gay" (meant derogatorily) Lindy Hop was created by done originally by the black American community in Harlem NY. It spread throughout the country, and eventually the world. For tens of years since its initial creation, Lindy Hop Was more or less a staple of many of American's community activities. For not just the black, but also white, Hispanic, Jewish, Italian, Irish, and other communities. Much has been written on this subject throughout the years. This simple blog post is not the place for an exhaustive history of the evolution of America's community's music and dances.
Touch your friends - Consensually
Close proximity to people that care for you, and whom you care about in return is valuable for your well-being and health. (Even touching strangers helps.) Though, proximity to friends and family is not the only thing that's meant when scientists say that humans are "social creatures". Social means more than conversation. Social means meaningful contact. Partner dance is an expression of that meaningful contact. Dancing is done at all because actual physical contact with friends and family is important. It forms bonds that are stronger than merely being present with others.
Source: "Platonic physical contact is valuable for your own health and well-being."
"Safely and appropriately cure your touch starvation with Lindy Hop" – Anonymous
To sum everything up
Yes, it's normal to dance with strangers. Encouraged really. Judgment-free space, no matter what you look like, who you like, or who you don't like. Social Lindy Hop isn't meant to be pretty. It's meant to be fun!