How should we behave the Muslims that do not practice Islam?

Nowadays, it is obvious that people who look like Muslim can be stated as mushrek depending on their attitude and behaviour. These people define themselves as Muslim and they are not aware of their mistakes. My question is : " How much suitable is it to greet them on feasts/ festivals which are special for Muslims? " Is it wrong to celebrate feast/festival and get in a dialogue with these kind of people by telling them that, this is a Muslim feast/festival. This feast /festival is for people who perform their prayers, fast and obey the rules of Allah. Could greeting them on behalf of telling the truth decrease our belief ?

It is not suitable to stigmatize people as mushrek before declaring, explaning the truth.
We are not authorized and we don’t have the right to split or group people as mushrek and non-mushrek.
We are responsible for explaining the truth and have a living adaptive to the rules of Allah as much as we can. Thenceforth,  it depends on those people. Meanwhile we should continue all routine activities including greeting / celebrating feast /festivals. This never decreases our belief. There is no objection to meet and accompany them. You can invite them to your home. You can try to tell the truth when you are together with them. It is not suitable to exclude them just because they are not  thinking like you.
Indeed, Allah has given people the freedom to believe or not to believe.
The relations which harm the belief are the ones with people who are at war with  Muslims, who exile Muslims and who support those.
These are the three red lines of us.
We should be on good terms with people who do not violate these borders, even non-Muslims.

“Allah forbids you not, showing kindness and love to those who have not fought against you on account of your religion, and who have not driven you forth from your homes. Allah loves those who are equitable. Allah only forbids that you make friends of the ones who have fought against you on account of your religion, who have driven you out of your homes, and have helped others in driving you out, and whosoever makes friends of them — it is these that are the transgressors.“ (Al-Mumtahanah/The Examined One 60/8–9)”

Please follow the link below to read the text on our site about relations with non-Muslims:
http://www.islamandquran.org/fatwas/relations-with-nonmuslims.html

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Date: May 7, 2012