Well, I've come to terms with the fact that Pathfinder as a game system is too tightly integrated with traditional magic to be able to easily convert to an arrangement that leaves out the spellcasting classes.
So here's my thoughts on how to include psionics without surrendering too much on the "pathfinder modern" setting I want to build.
My setting uses all the races from Advanced Race Guide (I should be able to find a place for all of them), plus the races from Dreamscarred Press' psionic books.
Humans and humanoids with the Human subtype don't have access to any kind of arcane magic, but they can use any psionics class from DSP's sourcebooks. Technically, humans can take any class with spellcasting ability, but never gain the Spells class feature of those classes (nor Cantrips, Orisons, or similar 0-level magics). Templates might override this restriction. Aasimar, tieflings, half-elves, half-orcs, and other hybrids have normal casting abilities. Some of the DSP races may also be barred from arcane spellcasting but that's TBD. None of this applies to divine magic; divine casters are mostly unheard of among the mainstream human population--but for every thousand human beings who claim to have actual power, there have always been a handful whose abilities are genuine (albeit still quite weak and not nearly as flashy, by most races' standards).
Arcane magic and psionics are similar disciplines but differ in the power source, which influences what effects are possible with each discipline. Arcane magic is powered by extraplanar energies. Psionics is powered by thought, spirit energy, or ki.
Divine magic is obtained by true belief in the gods (clerics and oracles), nature as a deity unto itself (druids and rangers), or a philosophical system (paragons, crusaders, blackguards, and renegades). The gods and their semi-divine servants do not interfere in mortal affairs, do not visit the material plane in avatar form, but can grant spells to their followers even over billions of light-years.
