Fitrah can be thought of as...
... the natural disposition/instinct which Allah created human beings upon that is not tainted or corrupted by external influences.
Linguistically, Fitrah (فِطرة) is:
الْخِلقة التي يكون عليها كل موجود أَوّلَ خَلْقِه
The innate nature that every newborn is initially upon
الطبيعة السليمة لم تُشَب بعَيْب
The sound nature that is not tainted by any defect/shortcoming
ما ركَّزه الله في الإنسان من قدرة على معرفة الإيمان
That which Allah Has instilled naturally in with regards to recognizing Eemaan
With this overarching definition in mind...
... the following concepts are considered to be examples of the Fitrah:
Belief in the existence of Allah as the One who Alone deserves to be worshipped
This subsequently makes Fitrah synonymous with the religion of Islam in certain contexts.
Proofs for this can be found in:
Deeds or actions that are considered to be part of innate, uncorrupted human nature
This includes:
matters pertaining to personal hygiene
Another Hadeeth narrated by Abu Hurairah shows the Prophet ﷺ refer to several things as being "from the Fitrah":
الْفِطْرَةُ خَمْسٌ - أَوْ خَمْسٌ مِنَ الْفِطْرَةِ - الْخِتَانُ وَالاِسْتِحْدَادُ وَتَقْلِيمُ الأَظْفَارِ وَنَتْفُ الإِبِطِ وَقَصُّ الشَّارِبِ
Five things are part of the Fitrah: removing the pubic hair, circumcision, trimming the moustache, plucking the armpit hairs, and trimming the nails.
Sunan Ibn Majah, and there are other Ahaadeeth recorded in other authentic collections with the same meaning
when Prophet Muhammad ﷺ chose milk over wine in the Night of Ascension
أن النبي صلى الله عليه وسلم أتي ليلة أسري به بقدحين من خمر ولبن، فنظر إليهما فأخذ اللبن، فقال جبريل صلى الله عليه وسلم: "الحمد لله الذي هداك للفطرة لو أخذت الخمر غوت أمتك
On the Night of Al-Israa (the Night of Ascension) the Prophet (ﷺ) was presented with two drinking vessels: one full of wine and the other one full of milk. He looked at them. Then he took the vessel which was full of milk. Thereupon Jibril (Gabriel) said: "Al-hamdu lillah (praise be to Allah) Who has guided you to that which is in accordance with the Fitrah (i.e., Islamic Monotheism; pure nature of Islam). Had you selected wine, your people would have gone astray."
Saheeh Muslim, Book 14, Hadeeth 1393
The natural state/condition that Allah Has created things upon
Imam at-Tabari alludes to this in his exegesis of an-Nisaa:119 (Arabic only) as a possible meaning for what Satan refers to when he says that he will order those who listen to him from mankind to "change the creation of Allah":
وَلَآمُرَنَّهُمْ فَلَيُغَيِّرُنَّ خَلْقَ اللَّـهِ
... and indeed I will order them to change the creation of Allah.
Surah An-Nisaa, Verse 119
And this is how homosexuality falls foul of the Fitrah - it goes against the natural state that Allah Has created things upon, as was made clear by Prophet Lut when he called his people to abandon their homosexuality:
أَتَأْتُونَ الذُّكْرَانَ مِنَ الْعَالَمِينَ وَتَذَرُونَ مَا خَلَقَ لَكُمْ رَبُّكُم مِّنْ أَزْوَاجِكُم بَلْ أَنتُمْ قَوْمٌ عَادُونَ
Do you go in unto the males of the world, and leave those whom Allah has created for you to be your wives? Nay, you are a trespassing people!"
Surah Ash-Shu'araa, Verses 165-166
In summary...
... there is no contradiction between the examples mentioned in the question, as they are all examples of what a human being is naturally inclined towards as long as their disposition has not been tainted or corrupted by that which opposes it.
