Thanks for your question.
I did not complete my early education in the United States but I did complete graduate school which allowed me to stay here on a work permit called Optional Practical Training. That provides enough time for employers to apply for work visas.
You are correct about security clearance issues. In the US, there is a set of regulations called the International Traffic in Arms regulations which prevents foreign nationals from working on many aerospace projects specifically in military and space applications or any dual use technologies (civil and military). For this reason, many companies simply do not hire foreign nationals. This set of regulations actually fall under export control rather than regulations on classified technology, etc. Any project requiring an actual security clearance is not open to foreigners as foreigners are not eligible for security clearances.
What I meant to say is that I've never experienced racial or religious based discrimination on a personal level from any employers. I don't consider employers not hiring foreigners as discrimination as their hands are tied due to legal issues.
To be able to work in the US, you need a company to sponsor a work visa. Many companies simply find this too cumbersome to do. But there are exceptions. Also, these will be companies that work on projects that don't fall under ITAR, which is tricky because ITAR rules are loosely defined as to what technologies are included. Companies can apply for ITAR-exemption for foreign nationals. But again, the process for this is quite cumbersome and many companies are not willing to do this. One company that hires Canadians is Gulfstream and they work on civilian aircraft.
The good news is that if you are able to be here on a work visa and the employer is willing to sponsor you to become a permanent resident, then you automatically become eligible to work on ITAR-sensitive projects after you get your green card.
So the short answer is, it is extremely difficult for foreign nationals to work in aerospace in the US. I was lucky enough to find a job that was not ITAR-sensitive and my employer was willing to sponsor my work visa. However, I applied for this while I was already here on a student visa and was able to use the practical training work permit that comes with the student visa to start my job after graduation while the paperwork for a work visa was being done.
The other thing is that getting jobs in the US is highly dependent on networking. Online job applications are not very helpful. So attending conferences, etc. where you might meet senior engineers or managers from the US who might be able to help your resume/CV get to the right person can be very useful. The opportunities that I've found open to foreign nationals has pretty much been through networking. Hearing of another foreigner working at a company through alumni networks at my university or meeting someone at a conference and following up to see if there are other positions open at their company. NASA Ames Research Center is another place with several foreign nationals hired as contractors. Again, its networking that is really helpful to hear of opportunities like that. I met several helpful people through attending the Space Generation Congress and the International Astronautical Congress. Both of those have programs for young people include travel funding available and networking opportunities. So if you're interested in space projects, I would check those out.
I am not sure what the situation is in Canada or Europe. I think its definitely easier in those places compared to the US (though I'm Canadian so I don't have any idea about visa problems in Canada). I had good luck with applying to jobs in the Netherlands in the past.
If you are still in school, doing internships is an excellent way to get your foot in the door. There are definitely internships in the US that are open to foreign nationals. NASA Academy for example has a few limited spots for European and sometimes Canadian students.
Hope thats helpful.