There's many reasons why soldiers aren't idolized as much today. For one, today we live in a society that values peace over war, we want cooperation and less conflict (in general). Soldiers are people that choose to go to war (it's not forced on them) and so to a lot of people who do value peace, the soldiers are directly opposing their belief in a peaceful world, by choosing to aid in the support to war. Now, a lot of soldiers don't actually go to war, but instead participate in international aid, which most people are ok with, but a lot of soldiers do go to war. For them, why should they thank or support someone who has chosen to fight in another country that they didn't want anyone to fight in?
The latest US wars have been shifty at best, the war on terror in Iraq and Afghanistan broke numerous UN violations that the US initially helped start, it was an illegal war. I dunno if the war has done much to protect the United States from terrorism, but it has created an extremely paranoid atmosphere in the US, where people are willing to have their government observe all their online activities in order to stabilize this supposed threat. It's almost undeniable that a very large reason the US went to war in the first place was for oil, considering the first non-military building they built in Afghanistan was an oil pipe. The whole thing with Syria and so forth, just makes the US unpopular with the global population, these wars aren't for protection, but to increase economic growth and power of the US, which is not really the way to go if you want less conflict.
The US does thank soldiers a lot though, the two national holidays (TWO national holidays) is a big example of that. The Soldiers do get paid a decent amount, privates are only payed $18,000 a year (but this is only for the first two years), while staff sergeants are payed $35,000. Officers are payed a considerable amount more, around $35,000 - 70,000. This is on top of food, weapons, equipment and so forth that the solider gets. This is only basic pay, but there are a few other things such as bonuses, special pay (for special duty officers), drill pay (for reserve soldiers) and allowances for living expenses.
So that would be my reason why soldiers aren't absolutely idolized, but I do believe they are thanked somewhat in the US.
EDIT: As for protesting at funerals, as far as I know that's mostly Westboro church, that's a totally different (and depressing) reason altogether.