I think you're slightly mistaken about what Ti does. You are still describing Fe, or rather Fi.
Fe/Fi.
This is so ridiculously Fi/Te that I don't know what to say further.
This would be an INFJ with a strong Fe, an INFJ with strong Ti would neutralize any strong moral judgments because that's what Ti does. I strongly suspect you're an INTJ however, because you're reflecting your tertiary Fi over Ti in your posts.
Cool! I hadn't looked at it this way. I'm not sure, though. Ti has definitely got a deciding role. It doesn't say "nothing is truth", it does the opposite, it actively seeks "truth" (while Ni constantly reminds us that it is not there). Ti in very basic terms is - What is important? It strips out information that it believes to be secondary or misleading and attempts to get to the heart of the matter.
Fe says a = bad, b - good (obviously I'm making a broad generalisation there), based on external (thus unchangeable) rules. Ti is internal - thus malleable because it is based on "my" thoughts not "the" facts (which are seen as objective by a Te user - so they would believe in things outside of themselves to be true - let's say statistics - while a Ti user may see statistics and decide whether or not THEY think they're true and say either - this looks right, or these have been skewed by something). Fe sees morals as objective and thus unchangeable. Fi sees morals as being malleable and they may allow their own personal feelings to mess with their morals - i.e. I used to believe cheating was wrong but then this happened to me and now I think there are cases where it can be justified. See to me, I can't imagine ever being able to change my mind on something that seems so "naturally and obviously true" as morals. But when we see anything as "naturally and obviously true" then that is our extraverted functions coming in to play. As Ni users, I think we are all very aware that there is no such thing as "naturally and obviously true", as reality is subjective. But we do need an anchor in the external world to create a stable identity (if we do not measure ourselves against the outside world we are unable to come to any conclusion on who we are because metaphysical thought depends entirely on the existence on perceived binary opposites, whether you consciously believe in them or not).
So, where was I? Fe sees rigidity in morals but THAT'S IT. All of our functions are entirely useless on their own. They work together (extraverted with introverted) in order to create a "whole" (because nothing on the external plain can be made sense of without reference to the internal plane and vice versa). So Fe works with Ni to say: These signs/clues I am picking up from the outside world are "bad" or "good". However, there is never a person or thing on the outside world that is wholly "bad" or "good", thus Ni takes this into account and no conclusion is made. For us to say "I don't like that person" we must disqualify some of the information we have taken in and labeled "bad" or "good" - what disqualifies to get to the heart of the matter? Ti.
I thought I was an INTJ too, and I agree it is confusing, I'm sure I still could be if I had another look at the functions and tried to see it. The main reason I have decided on INFJ is from looking at other forums of different types talking to each other.
I'm not saying INTJs are unpleasant, I'm sure they're very nice in person, but they can seem very rude over the internet and I even once saw one complaining that her boss had told her that her colleagues had reported that she was rude! If that happened to me, I'd be absolutely mortified! I'm not sure I could go into work the next day, knowing that people in my office had got an impression that I was a rude person (thus "bad" person). It would be humiliating. However, the INTJ response was "if I was not like this we would never get anything done. They need to wake up and live in the real world. How dare they make it look like I've done something wrong when if it wasn't for me the office would be inefficient". See what I mean?
However, I am a type one enneagram (if you believe in all that stuff, can't say I do, really) and this type is known for being very sensitive to any ideas of not being "good", finding the idea of being a "bad" person humiliating and torturous. I'd suggest that an F type is more likely to be a type one, for the reason that F types essentially just think relationships/people/morals before they think logical fact. They think both, it's just that they prioritise relationships/people first - seeing this as more important (not necessarily in a kind way, though, depends on the user). So if you see Fi/Te then it is conceivable that I am an INFP.
EDIT: Just had this thought. Ok, Fi/Te and Fe/Ti could, conceivably, show similar behaviour depending on the situation. In fact, Fi/Te and Fe/Ti could definitely behave in the way I described of deciding who is going to be in their lives and trying to avoid people who they do not like. But it is the way the person comes to the conclusion that is important. All of the functions simply describe how we process information, they do not define what conclusions may come up with but they do influence them a lot. So Let's say I used Fe/Ti. How have I decided that I do not want a person in my life? What I have done is said: This person is not morally fit and proper. Now, people accuse me of taking "irrational" views on people. Because I do not take people's actions or what they say into account when making my decision. A person may appear to be nice on the outside but actually they have a motive for appearing this way. Think ESTP. They're very manipulative and my former boss was a lot like this. They say all the right things and do all the right things but they're doing it for all the wrong reasons (according to what I judge to be right and wrong). They have ulterior motives. So do INFJs sometimes, but they're ulterior motive us generally judged to be "for the greater good" rather than "what I deserve" or "what I can do" or simply "because I can". So I will "just know" what their motivations are from first meeting them and disqualify them based on this regardless of what they go on to say and do. If their motives are not pure, I don't care what they say and do. It doesn't make them "good".
Fi/Te may also disqualify people, but it's a little harder to do so. It depends on which is the more dominant function. Plus, without Ti, Fi/Te may (in some types) see no need to disqualify. Fi/Te judges a person depending on how the evidence before them correlates with their inner value system. So they will see a person who does and says all the right things and say that's what's important. To me, that's definitely not what's important. Essentially, Fi/Te may say "I don't want to be around this person because their actions and words offend me". Fe/Ti says: "I don't want to be around this person because their motives offend me.
Ti makes the decision according to what is at the heart of the matter and what it judges to be important. In and INFJ, a person's moral fabric is "what's important". They "see" this moral fabric by using Ni/Fe to intuit their motives. They may then say "this person is not going to be in my life because I don't like what's going on inside them". They may even be annoyed when the person does or says everything right and is invariably liked by most, because they feel that people are being fooled, or that the person is undeserving of the respect they gain and opportunities they are given because of that, due to the fact that the person's intentions were not pure.
Te, on the other hand, makes decisions depending on whether a person is saying and doing things that are justifiable and "good" according to their value system. They may not see ulterior motives. However, they will be annoyed with actions/words that offend their value system REGARDLESS of whether the person intended it that way. For instance, I once shouted at a friend of mine because she had upset me. I then felt very bad about it because I had done it the wrong way. While my initial complaints were valid, the way that I had expressed my complaint was disproportionately harsh. I told two friends, an Fi/Te user and a Fe/Ti user.
Fe/Ti said "you had the right to do it, don't worry about how you did it, your intentions were correct/good/moral".
Fi/Te looked at me aghast! "Well you need to make it right! Apologise!" I already had apologised in this case, but Fi/Te focused on what I had done, not what I had meant to do. Fe/Ti focused on what I had meant to do, not what I had done in order to judge. Both judged according to morality, but they judged different parts of the situation.