Avoiding behaving like non-Muslims has to be put in the right context, especially since the word "like" automatically means the prohibition is contextual (conditional), and not conceptual (under all circumstances).
In Sahih ibn Hebban and Sunnan Abi Dawood, the hadith says:
قَالَ رَسُولُ اَللَّهِ صلى الله عليه وسلم مَنْ تَشَبَّهَ بِقَوْمٍ, فَهُوَ مِنْهُمْ
The Prophet (prayers and peace be upon him) said: "He who imitates any people (in their actions) is considered to be one of them.”
This imitation is not simply actions, but actions and beliefs. Allah says in the Qur'an 2:118:
وَقَالَ الَّذِينَ لَا يَعْلَمُونَ لَوْلَا يُكَلِّمُنَا اللَّهُ أَوْ تَأْتِينَا آيَةٌ كَذَلِكَ قَالَ الَّذِينَ مِنْ قَبْلِهِمْ مِثْلَ قَوْلِهِمْ تَشَابَهَتْ قُلُوبُهُمْ
Those who do not know say, "Why does Allah not speak to us or there come to us a sign?" Thus spoke those before them like their words. Their hearts resemble each other. We have shown clearly the signs to a people who are certain [in faith].
"Those who do not know say": This is their action. It is apparent to others.
"Their hearts resemble each other": This is their belief, and the resemblance.
Suhail Hasan said in his book "Al Sunan wa Al-Athaar fi Al-Nahy an Al-Tashabbuh bi Al-Kuffaar" (roughly translated as The sunnah and the traditions in forbidding imitating the non-believers) that imitation falls under two categories:
- Permitted (halal)
- Not permitted (haram).
He further elaborated that imitation, which is permitted has to follow certain conditions:
It should not be an imitation of their traditions that only non-believers do, and these traditions distinguish them from others.
It should not be part of their religious beliefs, unless the Prophet has also done it (e.g., fasting on 'Ashoora or praying two raq'aas upon entering the masjid).
It should not be a matter that goes against Islamic teachings or commandments, and it should not be a matter that Islam explicitly forbids.
It should not be related to celebrating any of the non-believers festivals.
Apart from that, one can do as non-believers do, long as it is accroding to what is needed or required.
So, in specific, you can stop for a latte in a room full of non-believers, you can follow your family traditions or your upbringing which fulfills the above conditions, you can practice sports, etc., long as none of these actions cause you to violate any of the above conditions, or go against Islamic rulings in general.