I know this poll can never really be statistically useful data in the proper sense, despite my measures to improve its quality (e.g. unchangeable votes, can't see votes until you've voted, finite polling time, vote names are public). But it is interesting to see the early trends remaining consistent even with far more votes.
I will say, it seems pretty telling that the distribution is the way it is for a group of people who skew, as folks are so keen to point out, in the direction of optimization, system knowledge, and awareness of 3PP and other such things. It would seem to imply that the average player is even less likely to be allowed to use 3PP, given the low probability that such content is even known to them. And, further, my overall intuition--that 3PP is generally not used--is not precisely accurate, but isn't wrong either. It's about evenly split between the first two options and the last option; you get a one-vote majority by combining the first three.
Although, let's not forget that we tend to skew DM heavy. While, as a DM, I have no problems with people bringing me 3pp, and often use 3pp in pretty much any game I run. I don't actually get to play very often. Which means that when I do play, I tend to use core D&D stuff, since, well, I HAVE that, and I haven't gotten to play with it yet.
I think if you were to ask DM's if they used (rather than allowed) 3pp, you'd find the numbers flipped. If nothing else, the shopping list of monster books from various sources will probably see some use at some tables. Never minding adventures or things like Griffon's Saddlebag for magic items.
For players, using 3pp means that you do have to jump through a few more hoops. 1. You need a DM who will let you do it in the first place. 2. You need to be in a position where you want to move beyond what the WotC books (presuming you're playing 5e) already offers - and given that you may play the same character for a year or more at a time, it does take some time to exhaust the options just in WotC for players which means that new and newish players aren't all that likely to be jumping up and down to play 3pp. 3. You need to be in a campaign where that 3pp actually fits.
I mean, it's all well and good that you want to play an intelligent skeleton (a PC in one of my games), but, that's likely going to be a harder sell to the DM than a dragonborn or a tiefling.
The point I'm trying to make is that using 3pp has a couple of additional hurdles in the way that make it probably less attractive to players. You need a player who is invested enough to go hunting for material outside of core, has enough experience with the system to have exhausted existing options, and has a DM who is willing to allow 3pp material. So, the results you are seeing here aren't really all that surprising.