how can I allow others to see my living relatives
Profiles of living people can only be seen by the person who entered them. This is a privacy feature, and FamilySearch does not currently provide any way around it.
In my opinion, the best way to protect people's privacy is to not put their information anywhere public. The internet should be considered 100% public, even its password-protected or otherwise "privatized" spaces, so best practice is to not put living people's information online, anywhere.
Profiles on FS for living people serve one purpose only: to connect to their deceased relatives. (The dead have no need for or right to privacy.) You can achieve this connection with a profile that just says "Mom" in the given name field, and absolutely nothing else. Unmarried and childless siblings don't even need that much, as they don't connect to anyone new.
Here are a few articles from the Help Center that might be helpful:
How does Family Tree protect the privacy of living people?
Who can see my living relatives in Family Tree?
What Family Tree features can I use for the living and confidential people in Family Tree?
Darlene Bills-Brady I recommend you minimize the information you have on living people. When you die, all the information you have on people marked living in FamilySearch will be permanently invisible unless someone else has your password and login. Use other platforms to share information on living people - or better yet, keep it completely off the internet and only do trees of living people on your computer. Even on Ancestry, I do not have most of my living relatives on a tree. Only if they have asked me to research their ancestors do I add them to FamilySearch and my Ancestry trees. Then I grab a photo from a public profile of theirs so I can do screen shots or screen shares of their tree with their picture and family as the anchor. I keep no record of births, weddings, etc for living people.
Can you make your tree public within FamilySearch Family Tree? No not fully ... But for purposes of collaboration - each record, Memory or profile you submit/modify/attach references your profile/contact information. So if someone is interested in your tree - they can 'see' you and your work. In Settings you can also 'Enable relationship viewing' - again so that if their is interest and someone clicks on your public profile - and also have 'enabled relationship viewing' - a path to the relationship between you both is displayed. I believe the part that shows Living people might just say 'Living' but for yourself it will show your name.
You can also use the social network sharing options to share/post pretty much whatever you want to share. The new homepage let's you add Friends for this purpose. But you do need permission of those you may want to reveal...
Do you have the permission for those living people - to share their info?
To avoid all the complex privacy/security issues - FS intentionally protects such info.
NO there is no real way to share that living info. By design.
But as mentioned in the following - all this is scheduled to change design in 2023: