I am wondering how the common person would act/react to a Turtle coming into town? How wildly known are they? Would they be mistaken for Lizardfolk as weird as that sounds? I am just curious as I couldn't find much information. I do understand allot of it is up to ones dungeon master but I thought it would be an interesting discussion and maybe if you are a DM how have you dealt with players playing as a Tortle.

I'm not sure. With the diversity of races in the Forgotten Realms, I'm sure that a Tortle would be a cause for some interest, but as long as they weren't threatening, then I don't think people would react any differently than if a Tabaxi or Dragonborn or Tiefling came to town.

First, lets define what a "common person"  is.  Are you thinking of a stereotypical medieval European commoner?  How much exposure does our theoretical commoner have to other races? One that lives in a cosmopolitan city like Neverwinter is routinely exposed to tieflings, dragonborn, and more is likely to be far more open minded than someone, say, from human dominated Cormyr or the Dales.  What if we start assuming something other than pseud-European fantasy? A common person of Eberron or Planescape is way different than Faerun / Greyhawk / Dragonlance. 

 What about dwarves or elves or halflings?  Humans, elves, dwarves and halflings are considered the "common races," so how they would react would probably be different than a human, given the difference in culture.

Well,, lets assume a stereotypical European-esk fantasy setting that's primarily human dominated for the moment. As a quirk, humans that suffer from racism in the real world tend to have blanket reactions to different groups - we tend to see people equally problematic when dealing with the jewish community, the black community, the muslim community, etc.  So, translating that to fantasy racism, I expect that they're reaction of a tortle would be similar to their reaction to an orc or a tiefling.  Anything from curious ("wow, you have a tail? What's it like?") to wary ("he's kinda scary, I'm walking over here") to hostile ("I'm calling the Watch!") to indifference ("Who cares? Their gold  pays just as well."), depending on the individual.  Some will treat the person as an exotic being, and others will treat them as just.. people. It all depends on the person.

I do find it curious that there's a comparison to lizardfolk at all, rather than dragonborn.  I presume under the assumption that lizardfolk are "evil monster races." Which is funny, because lizardfolk are actually Neutral, not Evil.  They're territorial and tend to react badly to random explorers trampling over their hunting grounds, but not evil. There's no reason why a community can't be on good terms with local lizardfolk.

Anyways, in my games, the various beastkin races are fairly common, so most people don't bat an eye at it.  There's a human supremacy group in the game that will make issues out of it, and dwarves tend to be suspicious of all outlanders (well, outseaers in this case). But overall everyone is well aquainted.

The thing to remember is that even in the "cosmopolitan" areas, it's still not just plurality human, but majority human.  Waterdeep, per 3e sources, is 64% human, 10% dwarves, 10% elves, 5% (each) halflings, half elves, 3% gnomes, 2% half-orcs, and everything else too rare to list.  Seeing even a halfling is a rarity, and seeing anything other than humans, elves (part or full), dwarves or halflings is *exceptionally* rare.  For comparison, New York City is 44% white, 25% black, 27% hispanic, and 11% asian.  

So for me, I find it helpful to keep in mind how someone Very Different would be perceived in society.  Let's say you have someone with full body tattoos and pink hair, multiple piercings, wearing half a furry costume, of a different ethnicity than is common for the area they're in.  That to me is my tortle.  How would they be treated in, say, a very small town in a deeply rural area where they know just about everybody in town?  Will they get stares?  Certainly.  Will the cops / guard swing by, to see what their business is, how long they'll be in town, and what's going on?  Certainly.  Will folks duck indoors with their children as they pass?  Possibly.  Will a business deny them service?  Possibly, but very rarely.  Will they get hassled about how they're not welcome here and it's best to move along?  One would hope not, but it's possible.

Now compare that to how the same individual would be treated in a metropolis.  They'll still get looks.  The cops / guards *may* check in with them, but it's exceedingly unlikely, they have better things to do.  Otherwise other than some looks and the same questions they've likely received 100 times, no one is likely to give them any different of treatment than anyone else, at least not to their face, unless they happen to have a specific personal hangup on something about them.

However as I mentioned initially, D&D is substantially less diverse than real life in the United States, generally speaking, in a default Forgotten Realms setting.  So take how you think someone very atypical would be treated, and slide it over one notch towards the more rural / less tolerant side of things, because a) someone of a different race is actually just as rare if not more rare, and b) it's an actual different race, it's not just a different flavor of human, it's an inhuman creature, which is inherently harder for folks to accept and deal with, due to the inherent xenophobia in all creatures.  That's my advice at least.