The US has 192 rural inhabitants per thousand, as opposed to 176 for Australia.[1] Australia seems significantly more urbanised if anything. According to your logic, we should expect to see more hate crimes. That's not what happens though.
Wikipedia's list of ethnic riots has 134 entries for the US(since 1857, as that's the first Australian entry(there's more US entries in the dedicated article)), and 8 for Australia. That's 0.41 per million in the US, against 0.33 per million in Australia. The modern population should be fine as an approximation.
I'm going to insert mass shootings, because it's always fun to point this out. Wikipedia has 181 shootings worthy of articles[3], or 0.56 per million. Australia has 13[4], or 0.54 per million. As you've pointed out, Australia has a lower population, so this probably means that smaller shootings are worthy of articles. Removing shootings with less than 5 victims(which wouldn't have an article if they were American) gives us 7, or 0.30 per million.
Going back to homosexuals, the US has 148 items in Wikipedia's "History of violence against LGBT people in the United States"[5], or 0.47 per million. Australia has 13 entries(and no dedicated page)[6], or 0.54 per million. I'd almost surrender that point, if Australia didn't have 100% less cults walking around shouting that god hates fags, and 100%(or 6) less mass shootings of homosexuals.
Admittedly, I truncated all my numbers because I'm lazy. Sorry.
[1]http://www.nationmaster.com/country-info/stats/People/Urban-... [2]https://en.wikipedia.org/wiki/List_of_ethnic_riots [3]https://en.wikipedia.org/wiki/Category:Mass_shootings_in_the... [4]https://en.wikipedia.org/wiki/List_of_massacres_in_Australia [5]https://en.wikipedia.org/wiki/History_of_violence_against_LG... [6]https://en.wikipedia.org/wiki/Significant_acts_of_violence_a...