I really am one to love the double standard that the republican party, and Donald Trump himself are held too.
It's not a double standard. Obama's travel ban was based in reaction to a very specific threat of terrorism (people who where part of a refugee program from Iraq were found to be plotting a terrorist event.) In reaction to that specific, serious security threat Obama placed the temporary ban on additional Iraqi refuges entering the country.
Trump is not reacting to a specific, imminent terrorist threat. He's reacting out of Xenophobia and unsubstantiated fear that refugees are stealing American jobs or making America unsafe. Further, since there is not direct security threat, he's violating the constitution by banning legal green card holders entry to the Country they have lawful access to (and call home) based on their religion. The first Amendment of the US Constitution prohibits such discrimination.
Next, the US Constitution places "common defense" as a third reason why "We the people seek to form a more perfect Union"...behind "justice" and "domestic tranquility". Link -> http://constitutionus.com
And it's the "justice" part that everyone is upset about. What Trump is doing is not just. And if he wants to revamp the refugee program in the interest of "common defense", that's fine. But take more than a week to figure out how to do it properly so you don't fuck up peoples lives with unintended consequences.
Trump has just given everyone another example of how unprepared, illogical, and irrational his decision making is.
Shit, you want to talk about double standards?! How about the Republicans suing Obama for using Executive Order to pass laws (after the Republicans denied him any sort of compromise)? Yet in the first week of Trump's Presidency it's been a new Executive Order every single day and the Republicans say "oh, it's not the same thing". Fucking delusional.