Consider for a minute that role playing games are largely based on the concept of allowing players to act out dangerous, scary, and/or heroic situations in a safe environment.
RPGs are often filled with things that would absolutely terrify us if they happened in real life - walking around in a world filled with violence, magic, Big Bad Guys, death, combat, intrigue, subversion, and just general conflict. Players get to act out scenarios and describe how they would deal with these monumental challenges, without actually putting themselves at risk.
As a very basic example, your character walks into a situation or a scene, is faced by a group of scary beings holding weapons. In real life, that would be utterly terrifying. But it's a core part of the game!
As a less obvious example, an NPC that has befriended your party is being deceptive and undermining your ultimate goal by helping your enemy. That would never be something I would choose to face in real life, but again - it adds to the game, and story elements that present challenges are a key part of why it's interesting.
Ultimately, the people involved in a particular game must be able to discuss freely and decide what is or is not acceptable. But consider this - I've played in many D&D games that involved things that are scary to me, personally. In effect, that's part of the fun - I get to work through how I would handle these things. I get to confront them mentally which can, in a sense, help me work through how I feel about them. I'm sure this is a common experience for many people who play RPGs, it just probably happens around things that are less obvious than homophobia.
Let's put this in context for your question.
In real life, a homophobic Russian might be frightening to you. But I'm sure there are many other scary things happening in your game, which add value to the story. Many of them may be purely fantasy-based, but some of them may closely echo things that actually happen in the real world (conflict between friends, people who try to manipulate you, and so on). Consider if this idea, too, can add value. Maybe the character's homophobia will somehow hinder his progress. Maybe he will have a change of heart because he experiences something that really shakes his core beliefs. Maybe he will somehow "win" in the end, by some trick of fate, in a way that actually somehow reinforces his beliefs.
So - before discarding something because it's frightening, consider:
- Talking through the concept with the player. Understanding why he wants to include this element, and how he intends to act it out. Make sure it is clear among everyone that there is a separation between the real player in the real world, and the actions their character takes in the game world.
- Talking through how this element may, or may not, fit with the overall plot you have in mind as DM.
- Doing a gut check with other players to make sure they're comfortable with the idea.
I know these steps aren't significantly different than the content of other answers, but I am hoping I can offer a different perspective on why you might want to do these things versus just immediately discarding the idea.