I'm in a homebrew game run by someone I met online, there are 4 of us and we all get along and we're having fun but lately, the DM has let sex and romance become a very large part of the downtime story even between NPC's. I love our actual main story and what we're trying to achieve but I can't think of how to broach the subject of seeing if we can turn down the sex without them feeling hurt, or if the other players even mind and I'm the odd one out. 

It can be challenging, especially if you're someone who likes to avoid potential conflict, but you just need to have an honest conversation with the DM letting them know you're enjoying the overarching story of the game, but the sexual aspects are beginning to make you feel uncomfortable. It doesn't even need to be an all players on deck conversation, it can easily be a one on one conversation. The DM should be wanting to make the game as fun as possible for each player at the table.

There is no real easy way to broach the subject, but it should most definitely be done outside of the game and not during game time.

/e They won't know what makes you uncomfortable until you tell them.

If your DM values your input, they will be happy to call a quick table discussion on the matter and come to a mutually agreeable resolution.

If your DM does not value your input, I would advise finding another DM.

Really, the GM should have asked if everyone in the group was comfortable with this sort of content before adding it into the game.  But since they didn't, I recommend contacting the GM by private message and let them know that you're uncomfortable with it and don't really like having it in the game.  If they ignore your concerns, or worse, get hostile about it, find a new group.

Also recognize, at least the way you're describing the campaign, all this coupling between NPCs the DM is describing isn't the actual direction of the story, these are sideshows the DM is putting on during downtime.  So really you're just asking your DM if they could handle downtime differently in the game.  Not so much derailing the DMs game since the game shouldn't focus so much on what the NPCs get up to as what the PCs do.  

No DM worth their salt actively wants to make their players dislike the game. Being honest about it not only opens a door for improving your experience, but it also has the benefit of helping the DM know what works and what doesn't for that particular table. Plus, it's entirely possible you aren't the only one uncomfortable and nobody else has worked up to mentioning it yet. 

If the group is a bunch of mature players, the comments will be taken in stride and adjustments made to ensure the environment is enjoyable and welcoming for all. And if it's an immature group, the pushback you get will inform you whether continuing at a table that doesn't take your comfort seriously is worth your time. It's a win-win situation, having an honest conversation with your DM. In the long run, everyone wins.

Others have the right way of going about it, but if you want the actual wording in a private message, here's how I would say it:

"Hello [insert DM name here], how's things?

Just wanted to pop by and give some feedback if that's OK. Loving the main story and the goals you've let us aspire to, but I was wondering if it would be possible to tone down the romance and sex a notch? I don't feel very comfortable with this, and would appreciate either it be reduced or if I'm told a scene is coming up so I can deafen my headset until it reaches its climax (no pun intended). If this is something that should be talked about with the group as a whole, I'm more than happy to discuss it.

Again, thanks for the session and the talk; I look forward to the next session. Enjoy the rest of your day!"

That's usually how messages with my Dungeon Masters go, and it's just a quick template for you to use and tweak if there's parts you find disagreeable. If you feel like the odd one out, hey, it happens and sometimes the need to leave will create an elephant in the room for the remaining players, but you're under no obligation to play something that makes you uncomfortable.

If you don't get the response you're looking for, you then have to make your choice. Either you grin and bear it, or you quit while you're ahead. Normally I would say to be courteous and thank your DM for the games if you do leave, but I believe anyone who's going to froth at the mouth about keeping the sex in isn't going to be courteous back. I don't want to judge too harshly, and this really is between you, your group, and the Dungeon Master.

I wish you luck in finding a happy medium!

This is why I frequently remind my players that I am always open to feedback and constructive criticism. I let them know that if they want more of something, less of something or they'd like things they feel are missing added in to let me know via DM or one on one chat. I also try to make it clear that I would never call out or make obvious who requested something, and would leave that up to them to decide if they wanted to announce or make clear that they were the one's who requested something. Admittedly, I am very lucky to play with a great group, but when they have asked for things, I always follow up on it and make adjustments to give them what they want. (By which I mean game play, subject matter, etc. Obviously if they said, "Give us all Vorpal swords and +3 plate." That's not happening.)

A good DM, IMHO, should work to make sure the game is comfortable and safe for every player at the table. It's difficult to have fun when something is making one or more players genuinely uncomfortable. He/She/They should also always be open to feedback from players.

I hope your DM is open to feedback, takes that feedback in stride and makes good use of it. Good luck, and happy gaming.

I agree with everyone. Warn your DM about it. 
You don't even need to make a big thing about it. 
Just say "I don't like all that romance and sexual stuff"

Also this is YOUR character. What ever the DM want to do, you control it. 

I don't know, if the DM start a orgy scene or what ever make you unconfortable. 
You could just say "Me (Valna92 or something) I leave the room and go to my room. Pick up my adventuring gear and I am looking for trouble in the nearby forest."

Usually the players are the ones that have the biggest control of the Game. The DM just narate what happen arround you. 
Heck your party could decide to take a trip and start living and the next country.

I have always considered that a good DM is a flexible DM and that is able to improvise on the spot.
If your DM is not able to do this. Maybe that will be a good chalenge for him and it will allow him to improve. 

Anyway I wish you, your DM and your whole group. Good luck and lots of fun on your future game. 

Hopefully talking to the DM will sort out the situation. Sometimes it’s hard with groups you meet online as opposed to playing with close friends. But as others have said, a good DM will tone it down or eliminate it ASAP  

I’ve heard too many RPG horror stories so I hope it isn’t the DM’s or other players attempt at acting out RL fantasies in game. If you bring it up to the DM and or players, and it doesn’t change, then you might have to just leave the group. 

Good Luck