Even with a proper sample, a survey has to ask enough questions to get useful information, depending on what you are trying to find out. A survey like the one above that only asks if someone liked or disliked FP+ leaves open a lot of other questions about why the responder did or didn't like it.
The first thing I would be asking is how many times a responder had visited WDW in the past and whether or not he had used paper FP. For guests who had used paper FP, I would be asking which system he preferred and some follow up questions about what features of each system he liked and disliked. For guests who hadn't used paper FP, I would ask what aspects of FP+ he liked or disliked. These follow up questions could include subcategories to bring out responses about things like advanced planning, number of FPs offered, selection of attractions, availability of same day FPs etc.
I would also be asking respondents when he made his reservations to see if satisfaction is greater for onsite guests who made reservations at or near the 60 day mark as opposed to guests who made the reservations later or only received their original FPs at the park.
Without a lot of this background information, I find the results of a simplistic survey like this to be somewhat interesting but not very conclusive of anything. The self selection bias makes them even less meaningful.
For example, if someone simply has a choice of like/dislike, someone who answers "like" might be saying "I like it, but it could be better", "I like it, but I liked paper FP better" or "I like it and I think it is superior to the paper FP system", or lots of other things. Similarly, someone who says they don't like it might be saying "I don't like it because I don't like planning in advance" or "I don't like it because I liked paper FP better" or "I don't like it because I think I should be able to get a FP for everything I want", or countless other possibilities. With enough information, someone interpreting the results can differentiate between things that could be addressed (like "I would like to be able to get additional FPs on my phone"), and things that are unrealistic within the constraints of attraction capacity and serving all guests (like "I want more FPs and no tiering").
I would also be including some questions about the guest's overall experience on his trip. A response of "I didn't like FP+, but I had a great time overall and will definitely be back" is a lot different than "I liked FP+ but I had a lousy time overall and will never come back". Of course there all kinds of points in between.
This is why a "dislike" percentage in isolation should not be at all surprising or troubling. There is no way that a company is going to satisfy every single person about not just the overall experience but about every aspect of the experience. I also think, and I have said this before, that for guests who have experienced paper FP (and especially those who mastered and made extensive use of paper FP), FP+ is starting with a distinct disadvantage. I suspect that the reaction to FP+ would be significantly different for a lot of people if it had been the first FP system instead of following paper FP. If FP+ had been first, people might think "I don't particularly like having to pick things in advance, but it is nice to be able to skip 3 of the standby lines at times that I can select to fit my touring style". Then if FP+ had been replaced with paper FP, people would be saying "What, now I have to take whatever time the system gives me and I have to wait to pick a second one. That stinks". If nobody had ever been exposed to a system that allowed certain savvy guests to get multiple FPs for some attractions while other guests were shut out, things like tiering and limits on the number of FPs would not be as controversial.
The bottom line is that, while simple online surveys like this can provide some interesting chat board fodder, any attempt to draw meaningful conclusions from them about what a company should or shouldn't do is pure folly. I have no doubt that the Disney company has much more meaningful data, and will make business decisions based on that data, not by counting up comments on websites.