I am not running or playing 5e. In 3e, I and other DMs whom I know used third party material. In fact, actually, used/allowed much more 3rd party supplements than WOTC supplements.
If I were to run 5e, it looks to follow the same pattern. At the moment, I might allow a few WOTC supplemental spells and backgrounds. In contrast, I would be using several things from Kobold Press. I would also be using
a) from EN Posters: [MENTION=2167]Khaalis[/MENTION] (Light Armored Fighter variant posted on this site), several things from David Gibson (a.k.a, [MENTION=37579]Jester David[/MENTION] here on ENWorld), a few things from [MENTION=2067]I'm A Banana[/MENTION] (his conversions of the 2e Complete [X] Handbook), and a few other items that I have found here;
b) material from the websites Forgot My Dice, Giants in the Playground, Natural Crit's Homebrewery;
c) some DM's Guild offerings including material from Joshua Raynack (Alea Publishing), David Noonan (former WOTC employee);
d) I would be looking at DMG Guild material that caught my eye from David Moore, Mathew Mercer, Joe Karpathian (Pantheon series), Diegobastet (3 Archetypes series), Sterlling Vermin, and TheLe, because some of their stuff looks like it might be useful for my campaign. I am sure there are some others that I might find interesting.