Every fandom has its ships being them homosexual or not.I myself have,but I put them apart for myself since I don't force it on others.But I don't like when I see people being homophobic (now we go on a different topic)
I don't strictly see Dante as an anime character,in terms of appereance.There are many realistic manga and anime.Regarding his outfit in DMC4 I don't consider it really cowboy-ish.First those trousers resemble the ones that bikers wear (this is the first image I got while searching them up so I don't think it's the same but I found some pants that really resemble Dante's,only the color differs)
Not to add cowboys don't even wear leather or lots of zippers and such.
Now,it's a matter of style preference and what the character likes to wear.
Don't tell me you didn't see those scene kids or gothics even once while outside.There are people who have their own style of clothing,depending on their personality and Dante being a stylish man from what we know,it would be normal for him to wear 'unusual' clothes and something that fits his personality and preferences. (he gives me a rockstar feeling too)
Don't tell me you would see Vergil dressed like that in streets of America,he is a rich man,but he spent most of his time by his brother's side.Not even rich men dress like him,they dress like bussines men,so just like in Vergil's case,he has his own style.
We live in times which don't restric people so much from expressing their own choices.
Of course I don't see him dressed as Batman or Captain America,but as I said,I don't see it as inconvenient,also not that much of an importance.Even though I also like casual clothes that still fit the characters,this won't change my liking towards them.It's a matter of taste and preferences.