Since they have been made into a PHB race they are no longer on the "shot on sight" level. There are also a bunch of more or less outcasts by now (I guess the drow mercenaries from novels you might have read among them) who have made it more reasonable that you might be given a chance. If you are using the story hook from LMoP I would suggest that you talk to the DM and the Wood Elf player about Gundren Rockseeker or Sildar Hallwinter having checked around and heard that your character seems fine for a drow. So while the first few nights on the road might have been tense, by now all the party should know that they can probably trust you.
Regarding tieflings: they are assumed by some to have a tendency for becoming Devil cultists or generally be up to no good. There is a saying about tieflings that goes "one's a curiosity, two's a conspiracy, three's a curse".
Overall I guess that when they are an obvious part of an adventuring group there is no big difference between how people treat a drow, a tiefling or a half-orc.
Regarding tieflings: they are assumed by some to have a tendency for becoming Devil cultists or generally be up to no good. There is a saying about tieflings that goes "one's a curiosity, two's a conspiracy, three's a curse".
Overall I guess that when they are an obvious part of an adventuring group there is no big difference between how people treat a drow, a tiefling or a half-orc.