>Will this scare off landlords and property management groups even if everything else checks out?

Maybe, unless your state includes being homeless or living in a shelter as a protected class for housing, they are free to deny your application for that reason.

>Will they even know it's a homeless shelter since all they'll be given is the address?

Probably. Maybe they won't care to check references or verify where you lived previously, but if they do, they will figure it out.

You are likely going to have a harder time finding housing because of your lack of rental history. Having a letter written that explains that you were homeless, you've taken XYZ steps to stabilize your situation and are now looking for your own housing can help. So can having a positive reference from the shelter or another case manager that you were a good resident, are working on stabilizing your situation, etc. If your community offers "Rent Well" courses or assistance to homeless individuals in finding housing, take advantage of it, they may have programs to educate and incentivize landlords, and supports for you.