In response to this:

This is fantastic news. Although I live across the pond, it doesn't alter the huge impact this change in policy is. If given and sent to the right media, then this message of gender-neutrality may force other main toy store conglomerates like FAO Schwartz and Toys R Us in other countries to pay attention, research, and possibly follow suit.

The fact of the matter is that while categorizing toys by gender market makes it more "convenient" for shoppers and brand names, it psychologically reinforces gender roles, stereotypes, and sexism in the toys, brands, and overall toy market. Over time, we have seen and realized how much gender roles not only stigmatized society, but also harm it by dividing genders. With this change in policy, you set a standard to families, including parents, by forcing them to review products based on their overall objective quality — to name a few, material; production; care for the littlest details; psychological messages — rather than expected enforcement of gender conformation and roles. There are many ways to be feminine, masculine, or in-between, and it's important for every generation, including our future ones, to comprehend that. Toys R Us UK knows this and laid down what should hopefully be the golden standard of toys.

If I ever have a kid, I would want him or her to play with as many good toys as possible and be exposed to them — this includes old Thomas trains, Chatty Cathy dolls, Barbie dolls, action figures, new generation and old generation, etc. I want my kids to know that's it's just as okay to play with a product "marketed to girls," "marketed to boys," and "marketed to anyone," period. Give me any factually GOOD product, and I'm good.

Now, did the brony community help influence it? I doubt the brony community was exclusively or mostly responsible for Toys R Us UK's change in policy, but don't be so quick to dismiss it entirely, either. The brony community, other products like Hasbro's Easy Bake Oven, societal influences like same-sex-marriage legalization (France and England recently legalized same-sex marriage, for example) and the LGBT altogether, and advocacy groups like Let Toys Be Toys (the one linked in the OP) have been in the news over the past several years for its gender-inclusive, non-societal-conforming messages and reminders that anyone can enjoy a good product or message regardless of audience. If anything, there's a chance the brony community might've lent a very minute (yet equally important, nonetheless) influence to Toys R Us UK.

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Source: Toys Я Us scrapping 'Boys' and 'Girls' labeling for toys