Does the word "out" carry sexual-minority flavour?

I cannot see the word OUT without thinking outing/coming out

It does by the way not sound very idiomatic to say out of bias, out of borders, out of propaganda

Apart, Beyond, Besides even Without sounds better to me - more here

The connotation is not just LGBT-related. You can come out as a bronie. You can be outed as a spy.

However, your friend is right. If your documentary is not about LGBT people coming out of the closet, then it is a bad choice for a title if your documentary is meant to play in US and EU.

For example, this hugely popular song works for all kinds of coming out, but it is nevertheless seen as an LGBT anthem:

I’m Coming Out — Diana Ross https://en.wikipedia.org/wiki/I%27m_Coming_Out

… so even if your documentary is about coming out as a Russian speaker, people will assume at first that it is about coming out as LGBT.

Also, one of the most popular LGBT magazines of the past 20+ years is called “Out:”

Out Magazine https://en.wikipedia.org/wiki/Out_(magazine)

The reason people hear an LGBT connotation is that we are 40+ years into a massive worldwide social movement that encourages LGBT people not to “stay in the closet,” but rather to “come out” and gain strength in numbers to resist heterosexual violence and oppression. Once you have “come out,” you are said to be “out.” You may be referred to as an “out lesbian.” You might know someone is LGBT, but you might ask someone else, “is he out?” You might be careful not to accidentally “out” someone who is in the closet, because by doing so you may get them fired, evicted, beaten, or killed by heterosexuals.

My understanding is that Russia is many years behind US and EU with regards to LGBT rights, so you may not hear your title in the same way that people in US and EU might hear it. But later down the road, you may hear it that way and personally regret the title.

But separate from the LGBT-related connotation, I really don’t understand your title and tag line, and I’m British and US American. Do you mean “[Coming] Out” or “[Getting] Out” or “[Run] Out” or “[With]out” or “Out[side]?” You may have to be more explicit because we don’t know as much about the project as of course you do. You may need to be over-informative in your own eyes, because all of your potential viewers are under-informed.

I recommend you consider creating a new title for your documentary. “Out” not only says too much about something unrelated, it seems to me that it doesn’t say enough about the actual work. A good title can be really hard, but it’s so important. It’s a handle that your viewers can use to pull your work closer to them. With your source material, it seems to me that you have a lot of culture and creativity to draw from, so I feel like there is a better title waiting for you in the aether if you continue to chase it.