I would say my (Ti) "value system" would be better put as a "system of principles." There are a few things that I am pretty adamant about because I've reasoned it time and time again and it just makes sense. I can see how this would be similar to, say, an ENFP's value system. They feel their values as much as I feel my principles. But perhaps it's not as...logical?...for them. If someone were to ask my why I believe what I believe, I'd be able to provide a well-reasoned argument for why it makes sense to me. I don't know if Fi in ENFPs works the same.
But I do feel things...very deeply sometimes. But I only give time to things that seem, objectively, to be weighty: worthy of emotion. It's all about perspective. I have
very littleno patience for emotional drama (and there is a LOT that strikes me as emotional drama), but if someone is going through a tough time and seems genuinely affected and is trying their best to keep on keeping on, they will have 100% of my emotional support. If you can face serious situations with a level head and calm demeanor, I will respect you greatly. And that's how I treat my own emotions as well. So sometimes it looks like I'm always a joker, always laughing, never taking things seriously, never "giving in to or acknowledging my feelings" but there's a whole other world deep down that's quite different.
Anyway, complex question! Of course, I can only speak for myself. And I had more to say than I expected.