Do we have to convey the message to non-Muslims individually or is it the duty of Muslim Communities?
What right do non-Muslims have over us?
Non-Muslims have an individual right over us. The Prophet (ﷺ) said, “Convey from me even if it be an ayah” . We may know few Surahs like Surah al-Ikhlaas. The Non-Muslims will hold us accountable for not conveying the message of Islam in our social circles and sphere of influence. These are sins on us. Our colleagues, classmates and people at workplace have right over us for being conveyed of this message.
Allah and His Prophet (ﷺ) did not just leave it as a command to convey the message, as Allah says in the Qur'an:
وَمَنۡ أَظۡلَمُ مِمَّن كَتَمَ شَهَـٰدَةً عِندَهُ ۥ مِنَ ٱللَّهِۗ
“And there is none more evil or oppressive than the one who hides the witness he has from Allah.” 
We are witnesses to the Qur'an and not conveying it is like hiding it. No one becomes more evil than the one who hides the Qur'an. Allah says about them:
إِنَّ ٱلَّذِينَ يَكۡتُمُونَ مَآ أَنزَلۡنَا مِنَ ٱلۡبَيِّنَـٰتِ وَٱلۡهُدَىٰ مِنۢ بَعۡدِ مَا بَيَّنَّـٰهُ لِلنَّاسِ فِى ٱلۡكِتَـٰبِۙ أُوْلَـٰٓٮِٕكَ يَلۡعَنُہُمُ ٱللَّهُ وَيَلۡعَنُہُمُ ٱللَّـٰعِنُونَ
“Those who hide what I have revealed after it has been made clear to people in scripture are cursed by Allah and cursed by everyone who would curse.” 
None of us want to be under the curse of Allah. if such verses do not touch us and make us feel contempt, we are indeed at loss. The Prophet (ﷺ) said, “Whoever hides knowledge will be branded with it a brand from hell-fire.” 
 Jami at-Tirmidi, Hadith no. 2669.
 Qur'an, 2:140
 Qur'an, 2:159.
 Abu Dawood, Hadith no. 3658.< Back to Questions