A definition of "homeless" is used which doesn't mean "slept in a gutter last night / will sleep in a gutter tonight".
Imagine that I let a homeless person sleep in my garage overnight. Do they thus become not homeless? And therefore not eligible for other consideration?
How about if they sleep on my kitchen floor?
I don't take an objection to supporting people who don't have a right to sleep somewhere, or who only very recently acquired one. It isn't a time to cut someone off.
I also don't object to buying a magazine from W H Smith or from Baron Sainsbury, who are not even slightly homeless.
I have a separate response to beggars which includes not taking responsibility myself for a decision to support them or not. Let's say that I toss a coin to decide it, but not while they're looking.
We have collectively been sneering at and suspecting beggars certainly since Sherlock Holmes's "The Man with the Twisted Lip" of 1891, in which a wicked man indeed commutes by train to the best begging territory, until an innocent person finds him out. It's not really credible then or now, particularly as he passes by a drug house every day which must be making a lot more money - it's in central London after all. Or what about Lazarus in the bible who just sat outside the rich guy's house all day, the lucky sod.