What is the cost of Obama lying about it?
The biggest problem is that he's trying to relieve Muslims of any responsibility when in fact they do need to take responsibility: they need to either clean up their faith or abandon it. How much we can expect each individual Muslim to do depends on how much danger they'd get in.
"Muslim Americans mirror the optimism of many American communities: Nearly three-quarters surveyed believe that most people can get ahead if they work hard, according to a comprehensive Pew Research study on Muslim American demographics and attitudes. And they are as likely as the general American population to report household incomes of $100,000 or more (14 percent of Muslims, compared with 16 percent of all adults). They are generally satisfied with their economic lot in life: 46 percent said they were in excellent or good shape financially, compared with 38 percent of the general public who said the same. And they’re almost as likely as the general public to have graduated from college (26 percent of Muslims vs. 28 percent of the general public.)
Contrast that with the economic situation of France’s Muslims, who suffer from a lack of education and employment opportunities. While data based on religious identity can be hard to come by in France because of the country’s prohibition on collecting data on its citizens’ race or religion, France’s national statistical agency found that in 2013, the unemployment rate for all immigrants was at 17.3 percent, almost double the nonimmigrant rate of 9.7 percent. A Stanford study concluded that a Christian citizen in France is two-and-a-half times more likely than a Muslim citizen with the same qualifications to get called for a job interview."
It's funny that they call them Muslim Americans and not American Muslims. I've never seen any other example like that. Atheist American? Christian American?

I think it's telling that the Muslim part is placed first, because they also identify as Muslim first and Americans second
Anyway it's not their outlook on economic opportunity that's very interesting to me. It's more their attitudes towards terrorism, atheists, gays, women and liberal democracy. Polls on those questions always produce awful results, even for the American Muslims
Again though, you shouldn't discriminate based on lack of education. If you want a better life and you are willing to make an effort to achieve one, you should be allowed to immigrate.
I only used education as a metric because it tends to correlate with not being a future suicide bomber, but it's not a great indication because we've also seen well educated terrorists. There needs to be a very accurate vetting system in place to reliably weed out the 20% of Muslims who are Islamists. If we can't do that, I think it's completely irresonspible to let in any Muslim immigrants
Then why do we have many assimilated Muslims who are happy to be in western societies?
That depends on what your standard for being assimilated is. I think a reasonable standard would be to expect them to understand the values of the enlightenment and their role in paving the way for scientific and moral progress in the west. The majority of western Muslims would not meet this standard, as they favor theocracy over liberal democracy and blasphemy laws over free speech.
Not necessarily, because you have to consider the unintended consequences. You'd have to prove that the good it does by reducing misogyny outweighs the harm done from more hostility towards Muslims.
Let's run the experimetn!
There's a difference between legitimate concerns and systematic government discrimination towards a religious group.
Government discrimination further isolates Muslims as 'the other' in their minds and in the minds of the general public.
The government already discriminates against Muslims, and for good reason. I'm pretty confident the FBI spends much more time investigating Muslims instead of Buddhists in relation to potential terrorism. Because being equally worried about Buddhists and Muslims would be insane. Discrimination is only bad when it's done on the basis of bad evidence, which has been the case historically in relation to e.g. race or sexuality.