First of all, everything I say now is based on 3th and 4th competitive. I know this is 5th generation forum, but I still think my opinion fits in this thread.
I have always used my favourite Pokemon, Milotic. I have been bullied, flamed and trolled many times, but I have never even considered not using Milotic. The good thing is, that I win most battles I play.
When playing competitively (and uncompetitively), I always use Milotic. However, if I use other Pokemon I like, they are replacable if it makes my team better. But if I really hate a certain Pokemon, I only use it when there is no acceptable alternative. But Milotic is on every team I have ever used.
I am lucky that Milotic is no Farfetch'd or Pachirisu. Milotic might be outclassed, but is perfectly usuable in OU.
I have used both Milotic and Vaporeon on one team once, and that worked out fine. So instead of replacing favourites, you could also sometimes use a favourite and the Pokemon outclassing it together on one team.
I know competitive battling is not about favourites, but it is my choice to use Milotic and I want to play how I like to. And if I get high on leaderboards and win often, why not? And if that makes me "semi-competitive" or "uncompetitive", people are allowed to say so. Sure, competitive is about playing to win, but I play competitive because I like to. And I only like playing with Milotic.
I like this thread, it is interesting to see other opinions than mine. And I support everyone to use their favourite Pokemon.