Among dozens of gratis Tumblr themes, I've hardly seen any that offers to display tags on the front-page. Have you? Can you provide some links? It doesn't have to be all fancy, like tag clouds.
Update (2017-04-08): the generator seems out of service at the moment.
Here is a tag cloud generator, that you can insert on your tumblr home page: https://heatherrivers.com/tumblr-tag-clouds
I've found some themes 1.there is Esten theme, it shows several (maybe 10) tags at the bottom, 2.a theme by Dominic Valenciana, idk the name, but I know that it shows up to five tags in top bar 3.leen themes has Sandy- theme that shows up to 12 tags in sidebar 4.and there was one theme I've found by searching 'tag list' or maybe 'tag cloud' on that 'search way more themes' in tumblr- it is a grid theme called photogrid or photoportfolio or something like that, you can recognize it because on the header image there is a title in which every word has a white background, and it is THE ONLY theme that automatically lists all your tags.