Umm, he gave you enough information to do the significance test yourself under standard polling assumptions.
No, he didn't use a particularly large sample size. But the way the sampling distribution works means that you pretty quickly reach the level of diminishing returns so his survey is a pretty good guide to whether there is a substantial difference in reactions.
Are his respondents trully selected at random from the population under examination (as all the statistical tools assume). Well no, not really. But neither are academic studies (either is a telephone/internet poll or undergraduates at fancy universities) nor traditional telephone polling. The fact that Pew calls up 10,000 people (or whatever to get the appropriate number of responses) can't change the fact that the people who take the time to answer telephone surveys differ substantially from the population at large. However, unless there is some particular reason to think that the group polled (undergrads, mechanical turk workers etc..) will have a different take on the question at large (undergrads probably aren't the right people to ask "Is a college education a useful investment") we still take the results to have substantial persuasive value.
Having said this I do think there is good reason to be skeptical of the studies conclusions. This study put the picture in a formal professional context. I don't care if your *employer* calls them fun pictures of people in our division/department everyone realizes you don't submit actually fun pictures but ones that reflect workplace norms. Even though employers often look at facebook pages it doesn't make them an employer webpage and while few employers would post a picture of someone good naturedly giving the photographer the finger or of a woman who had participated in a wet T-shirt contest many years ago in college few would care if they were published on a non-executives employee' facebook page. Worse, the question asked about an employee chosen picture.
So who would SUGGEST it was appropriate to submit a breast feeding picture to your employers webpage? Unlike actually breast-feeding in public which, while you know it may make some people uncomfortable, can often be the only way to feed your child while going about your professional business, the only reason to submit a picture of you breastfeeding is to make a point about the matter. Also this is very unlike breast-feeding on your facebook page (you aren't trying to force the image on purely professional contacts only "friends") which is theoretically aimed at friends. So I tend to suspect the only people who will find that an appropriate thing to do on an employers webpage are those who thoroughly support the point being made. Anyone who has a view somewhere in the middle, e.g., it seems unprofessional to them and makes them feel awkward but understands that there isn't really another option for mothers in many contexts and if that's the picture you share on facebook they don't have to look, is stripped out by the language suggesting this is self-selected for the employers webpage. Since it is those who are on the fence which are probably most influenced by supposedly extraneous factors like the person's race this language tends to particularly avoid.
Personally, this is the problem I have with the MANNER some women choose to breast feed in public. The fact that certain people feel uncomfortable about it isn't a good reason for mothers to endure substantial hardship feeding their children. Just as the fact that working with someone who privately has strong views about a controversial topic (religion, atheism etc..) isn't a good reason to try and clamp down on personal bloggers or *private* political conversations between friends overhead in the office. However, in both cases there is a reasonable duty to exercise this freedom with reasonable respect in the office place. You and the guy down the hall and three other guys at work might bond over Jesus and maybe that sometimes makes the loan muslim feel a bit uncomfortable when he over hears you guys talking at the water cooler. Well his discomfort shouldn't stop you from chatting with friends even in the office. On the other hand if you go out of your way to shove it in his face, talking about it loudly when the whole office goes out for drinks or switching to that topic when he shows up it's your problem.
Similarly, taking reasonable steps to be discreet when nursing your child (being as least revealing as possible, asking if people mind....if you only occasionally have short meetings like a professor trying to avoid breastfeeding while a student is in your office....not having a child not totally sure if the last one is reasonable...trying isn't moving mountains and doesn't mean putting up with a squalling child) is required by professional courtesy and avoids the appearance of deliberately thrusting your breast feeding in someone's face. Worse is when some women use their breast-feeding to implicitly suggest that those women in the workplace who couldn't or didn't breast-feed their child for a similar length of time aren't as good of a parent. Unfortunately, some women who take themselves to be advancing the cause of breast-feeding do it harm by using the background understanding that sometimes a child needs to be feed at times privacy would be too professionally costly to deliberately thrust their breast-feeding in the face of those in the workplace or who couple their breast-feeding with constant talk about how healthy and better it is (perhaps not realizing the implicit insult they give those who didn't/couldn't).
This is sad. For instance, my wife who works in an academic profession and would never dream of saying no if a fellow professor asked if they minded if they breast feed, can still be startled when someone just undoes their shirt. I personally would be offended at the lack of a nod to a respectful request. Hell, I would ask during a meeting if the other party minded I use the restroom (though they better come up with a good reason to object...it will only take 1 second...and I think anyone who objects to breastfeeding has the obligation to take up the cost of avoiding it...they have to offer to come back in 10 minutes not expect the mother to wait). The reason it's ok to breastfeed but not just flash people randomly is that you need to feed your child...you don't *NEED* the other person to watch and if *THEY* care about it enough to undertake the burden of not seeing it's not proper to force it on them. The existence of these women makes it harder for all women who need to breast-feed and unnaturally politicizes what should be a simple matter of reasonable accommodation to need.
And of course there will be *some* implicit racism in reactions (though it may be fairly small). People are implicitly racist. Even by a very young age we react differently to those who look like us. We are implicitly racist about support for the poor (favoring it more when they are the same race) but I would be stunned if we were more implicitly racist about breast-feeding.