Private Profile, Public Lists

Is there a way to make certain lists public while keeping profile private, other than the share link option? The share link doesn’t allow other Trakt users to like the list so that they can follow it

The share link option is our solution to doing this.

So how do they like the list, for easy access rather than requiring the link each time? I must have missed something I needed to do to allow them to like it as it seems to be greyed out.
It’s a list I want to regularly update for them, but don’t want to have to make my profile public to every Joe Blog that comes along lol.

Anyone have any ideas?