As far as I remember from my one year Russian class, голубой (light blue) is used to name the color but also is a slang term for gay people. Are people wearing bright blue clothes are biased or considered gay in Russia?
No, it's not considered gay at all. Maybe schoolkids draw these comparisons, but it's not even a material for a friendly joke/mocking.
Earlier, in '90s or '00s, pink clothes could be considered gay, but with hipster fashion having reached every big city in '10s, it's also absolutely ok now, unless you're one of the underclasses.
In smaller cities, like less than 50K people, or rural areas, pink might be seen as womens clothes and be a trigger reason for negative attention.