you are free to draw rangloi outside your flat

2) your neighbour would be a fool if he were to oppose drawing of rangoli outside residence of flat owner

3)you have merely used enternace of your flat for beautifcation purposes

You have every right to display your faith within your property which includes the door. However, in apartments the space outside the main door of the house is a common area where the rangoli cannot be drawn without the consensus of all the members of the apartment.

Dear Concerned,

No - by display of Rangoli - a neighbor should not abject unless you have blocked his space to step out of his house.

It is suggested not to Argue with people of such ugly mindset who can go to extent of connecting Rangoli with Religion

Best of Luck

However, in apartments in urban cities where people from different faiths could be neighbours, what is the "legal" margin for the house entrance? Can a neighbour pick up a fight saying that I am displaying my faith outside my house?

You are living in India and not in any foreign country that your neighbor will object t the Rangoli drawn in front of the entrance of your house.

Your neighbor has got no rights to interfere in your personal life or belief or the traditions that you may follow.

You can proceed with it as per our own will and wish, if your neighbor objects to any such thing, you may issue a legal notice asking them to refrain from interfering in others business.