The disbelievers invite muslims to disbelief by stating that if you worship other than Allah you will be on their way, the muslims response is we do not worship what you worship, we have our own way which is to worship only Allah SWT.
These simple words purify a person from associating partners with Allah in worship. They bring the aspect of Islamic monotheism to the heart of the believer and these words remove any shirk from the entire being of a muslim.
We as muslims do not worship what the disbelievers worship like idols, people or any aspect of creation. A muslims worship is for the Creator of all that exists Allah SWT. This means a muslim cannot and will not worship false gods and will never worship false deities as they have no power, authority or knowledge to bring benefit or harm to a person.
Only Allah SWT has All power, authority and is All knowledgeable and can bring either benefit or harm into a person’s life depending on what is in the hearts of the people. This requires people to have clear good intentions, words and actions towards the creator Allah SWT and also the same good intention, words and actions for the people.
This will free a person and bring righteousness and freedom from shirk into their lives as no one can harm Allah SWT, the people only harm themselves through ignorance and disbelief when in opposition to Allah SWT. That is why only Allah SWT has the power to bring either benefit or harm into a person’s life depending on the condition of the heart of a person.
The disbelievers have their way and they choose disbelief in Allah SWT and his messenger Prophet Muhammad peace be upon him. The muslims have their way i.e. Islam and belief in Allah SWT and the messenger Prophet Muhammad peace be upon him who showed us the way to seek the face of Allah.
To you your way and for us our way means the disbelievers choose disbelief and have their own religion and muslims have Islam and the way to seek the face of Allah i.e. the religion that is only accepted by Allah SWT.