I'm American and I admire anyone who is able to speak a second language. Pro-job on moving to another country there no one speaks your native language. I've always wanted to do something like that and plan on accomplishing this some day.
You can't get around the fact that people do judge you by your accent, just as likely as by skin color, or the clothing that you wear. Things that people can pickup with their senses they will end up making a judgement. How critical that judgment is depends on the person. The best that I recommend to you is accepting the idea that you're being judge and dismiss the irrational judgement as irrelevant.
You can't help the person you're talking to has had a low level of exposure to the accent. You can't help their limitations of understand you. These things are out of your control. What is under your control are how you feel about the interaction. They may judge you but that judgement is irrelevant to your feelings because they're not inside your head. You're in control of how you feel.
As for repeating yourself, yeah there are some as*holes out there that will do that. I work with a latino woman and she has a strong spanish accent and I ask her to repeat sometimes too. I definitely don't mean to do it to make it difficult for her. It's just difficult for me to understand her sometimes and asking her to say it over again is kind of like a reflex. It just happens.
Regardless, I admire both you and her for learning a second language, and moving out of your home land to some place completely foreign. A lot of Americans wouldn't do that because it would be too difficult. Thanks for staying here for 4 years and putting up with some of the as*holes we have living here. Please don't let their actions speak for all of us.