Having observed the RP that Dominik Mentioned, I believe it was quite fine from all sides. I can see times where it will be different, but that will depend alot upon situation and location.
From what I understand of the Ilmater faith, is that they will give succor to anyone, including those who are openly in opposition, for that is their way. They do not judge, nor try and turn people from their chosen path, they just assisst all those in need. Now, this does not mean they are complete pushovers, but the Ilmatarians who actively work to defeat (through violence) tyrants, or evil-doers are confined to a small section of the order (the Knight groups or paladins usually). This does not mean an Ilmater follower will not defend themselves though. Though, one of the main reasons Ilmater is part of the Triad is that with Torm and Tyr actively fighting evil, Ilmater can concentrate on what he does best.
The other thing to note was the RP was in the Market Square. In a lawful good city such as Waterdeep, I would suspect the good people can tend to their faith and flock, and leave the "keeping of the peace" to the guards appointed to do so.
As for Lovitarian reaction, well that will be varied. I have had times when my evils have been as polite as can be to a Good char, just to learn more about them, what makes them tick....and what their weaknesses are. Other times - and this may be the majority of cases, they look at them with scorn, and would not even acknowledge their existance.
It all depends on the situation really. I tend to be careful with my RP in MS, simply because there are too many eyes on you (I mean that IC).Guards will be watching you, more than the known good chars etc. Just because they are tolerant of other faiths, I am sure most guards might be happy to "accidently" slap an openly evil person in the dungeons, just as a reminder. Of course this won't happen with the code, but that is not the point of course.
Still in the end. The RP that Dominik mentioned, in my opinion looked good, everyone got involved, and players got to explore their charecters and their faith. Though I would suspect, that if things came to blows, then quite possibly the Loviatarians would have wanted to beat a quick retreat, because, the whole of Waterdeep would generally side against them.....
But thats for another day
Ilissa