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Dawah by nature is transitory.
If we look at the Makkah period it has just the nurturing of faith - Tauheed, Risalah, Aakhirah. Things like major sins, for example drinking, are present but nothing is being said about them.
Islam is a journey, and a mighty one in that. We all travel together but there are different levels.
We should not demand the highest level from all.
There was this incident of a Bedouin who just wanted to do the minimal part and beloved Prophet (PBUH) said that if he is true to his promise then he is a man of Jannah.
So many people in India entered the fold of Islam due the efforts of the Sufis (and of course the traders.)
There Islamic training is being done now.
So we got to go ahead with our Dawah and leave the perfection, or even initial training to those who are adapt at that task. Jama-'at-ut-Tabligh is a nice effort for that at the mass level for simple minded people.
I suppose this should work even in the west for everyone there is not a deep intellectual.
I understand the concerns of the OP - people pay too much attention to other people's shortcomings.
It is true that we should not ignore slightest lacuna in our beliefs for it might destroy your faith but while thinking of that aspect we ignore the other aspect. That is, faith even if we have a smallest ingredient of it has the capability to take us to Jannah one day.
I do understand the point raised by brother NNoor. Actually we need not bother about it. If someone is stuck at the door of Islam because of the terrible fate of a Murtad then, in my view, this will be a case in rather few cases. Let us ignore them. The task in front of us is gigantic and we got to go ahead.