Conflicting schools of thought
There are many techniques that were taught by the Buddha and also later, other techniques were developed by Buddhist teachers over history, that are based on the Buddha's teachings. You are right that some of these techniques may appear to be in conflict with each other.

However, we must understand that each technique is used for a particular purpose, for a particular situation, to cater for a particular need.

It is just like how a master chef uses various techniques to craft the best results based on the needs. Sometimes you need to boil, sometimes you need to bake, sometimes you need to fry and sometimes you need to sautee. These techniques are mutually exclusive but used at different times to achieve different results.

You can find guidance on the basics of insight meditation in the booklet entitled "How To Meditate" by Ven. Yuttadhammo. This technique is used to gain insight into the workings of dependent origination. Also read "The Way of Mindfulness" by Ven. Soma Thera, which is an essay that discusses the Satipatthana Sutta. This the technique that involves noting.

But you can't progress in insight meditation, if you are strongly assailed by the five hindrances. To solve this, one technique is in the Vitakka-Santhana Sutta which teaches the forceful removal of unskillful thoughts. Forceful removal of thoughts is not part of insight meditation, but if you are too disturbed by unskillful thoughts, then you need to forcefully remove it.

To eradicate the hindrance of ill-will, you can use Loving Kindness (metta) as the technique for eradication. Intentionally generating thoughts of loving kindness is also not part of insight meditation.

For overcoming lust (as a hindrance of sensual desire), you can use the contemplation on unattractiveness (see this question). But too much of it may lead to negative thoughts of suicide, in which case, use the mindfulness of breathing (see this answer) to counter it. Intentionally contemplating on unattractiveness, is also not part of insight meditation.

Also, samatha meditation (see the article entitled "Entering the Jhanas" by Leigh Brasington) is yet another technique used to calm the mind, and create focus and concentration. This is yet another technique that could help insight meditation. But it can be developed on its own too.

If you are continuously disturbed in every way in meditation and cannot progress further, then the technique to solve this, is the development of virtue (sila) outside of meditation - see this answer for details.

So, although different approaches appear to be conflicting with each other, they are actually complementary. The Buddha taught the practitioner to be multi-skilled. That's why there's the Noble Eightfold Path, rather than a Noble One Single Technique to End Suffering. No one technique is sufficient to achieve the results.