I'm a native Finnish, altough I have a passport from a different country. Currently I live in Germany.
I have seen all sides from Finnish life, at first being a worker, then a director and finally a business owner. I always have had an open mind, but I can tell its true when you think the companies have problems hiring foreign people. Thats is absolutely true and I'm ashamed of that. Problem is that Finland has always been far-away-country, the Finns there happily (and sometimes not so happily) between Sweden and Russia. Until Nokia Corporation got into international business Finns were quite separated from Europe. Finns were always thinking what are those people in foreign countries thinking of us? It wasn't usual to have too many foreigners and if you were a black guy - people would stare like crazy (I'm white, but I know...). Everything started to happen quite fast in the 80's/90's and in a cultural way Finland is slightly behind of Central Europe (feels bad to say, but its true). But, don't get me wrong - Finland is in my heart and I love the country and the people. You will certainly find companies and people who are open minded - who will see the cultural richness is the benefit for the company. I guess most of the people who act racist way are just scared of the outside world. If you meet such people, please don't consider them to be the majority. Also, its good to remember there are Finns who had bad experiences with some foreigners, usually having had problems with Somalians, Gipsies (I had those problems as well) etc. This easily creates suspicion when they meet people from other countries or cultures.
There are also many Finns who are scared to talk English, even if its good - we were taught in schools to follow exactly the correct structure to create perfect sentences in English - that got more weight than actually talking. So basically some people are afraid to communicate with foreign people, and most of the Finns are anyway slightly shy. Give them few beers and you see a guy who will talk with you in any language
I think good way to avoid rejection is to avoid small places - in bigger cities there are more opportunities and people are more open minded. Sometimes even Finns experience "racism", if you are from Helsinki and visiting some rural village - they have a certain image of you and may even behave quite aggressively. Basically, Finland is bit more rough country - less culture, sometimes more aggression - but good point is, if you get friends they usually are long term good friends. Through the friends its often easier to get some jobs - so I would recommend being active, having some hobbies etc. and seeing people. If your own personality is open, you don't let these bad people get you down - you will eventually find a job. But, you should speak at least one of the languages; Finnish, English or Swedish. Sometimes even German or French could do, but in general English should be enough for basic jobs - or specialist jobs. Most big companies have one official language, and that usually is English - meaning you won't need to speak Finnish. I have had great problems learning German, so I can understand how difficult is to learn Finnish - which is even more difficult!
Wish you all luck!
CP