First of all let us understand who is a sanatani.
One who believes in Vedas and performs the karma mentioned in them and purifies his consciousness(i.e attains chitta suddhi). Purification of consciousness is to achieve brahma gnana which will give us the status of Jeevan mukta.
Now on to our next question. Can we just perform karma alone and not long for gnana?
The answer to this question is a resounding no from sri krishna himself
The misguided ones who delight in the melodious chanting of the Veda without understanding the real purpose of the Vedas think, O Arjuna, as if there is nothing else in the Vedas except the rituals for the sole purpose of obtaining heavenly enjoyment. (2.42)
Now another question to ask ourselves is can we not perform karma and long for gnana alone?
Again the answer to this is a resounding no from sri krishna
One does not attain freedom from the bondage of Karma by merely abstaining from work. No one attains perfection by merely giving up work, because no one can remain actionless even for a moment. Everyone is driven to action helplessly indeed by the forces of Nature.(3.04-05)
So based on our questions and answers by sri krishna(paramatman) to us we need to attain a fine balance between karma and gnana to become jeevan mukta.
Now to the main question. Will we be called a sanatani if we follow only Isha upanishad and respect other texts without doubts?
Yes you will be a sanatani. The following points will try to correlate the text in Bhagavad geetha with Isha upanishad.
Isha upanishad mentions that the way to escape the state of doing works is through work itself
Let a man wish to live a hundred years here (in this body) performing works; thus will an evil deed not cling to thee, while thou art a man; there is no other way but this by which to escape the influence of works.
A person performing karmas with intention of getting the result will have positive output attached to him which will help him in this life or further lives. If he performs karma with intention of purifying his consciousness then the result of work will not get attached to the person.
Isha upanishad explains the gana that we receive as following
When to a man who understands, the Self has become all things, what sorrow, what trouble can there be to him who once beheld that unity?
The above paragraph mentions the state that we will be in once we attain one true knowledge and become Jeevanmukta.
So even if we hold on to one principle our whole life and it is in sync with what parabrahma asks us to to do to become jeevan muktha then you are sanatani without any grain of doubt.
Respecting different thought processes and being tolerant towards different things are always ingrained in us sanatanis. So there is no need to demean any other text that does not confirm to our beliefs. Listening or reading it and being happy in amazement that how many ways that are there to understand of the glory of lord is the ultimate aim of living in this world.
Developing the view of vasudaika kutumbam and everyone as brothers and sisters will help us to put aside our differences and help each other to reach the ultimate state of being jeevan mukta.
source for Gita : Bhagavad geetha
source for Isha upanishad: Isha upanishad