Make the choices appealing
In brief, non-supernatural characters are still good to play, provided that they have their own advantages and extraordinary abilities.
In regular D&D 5e (as your question is tagged), players can choose to be wizards or clerics or warlocks, and bend reality to their will using magic. Or they can choose to be fighters or rogues or barbarians to exercise martial prowess or skill-based expertise. While the spellcasting classes are powerful, the non-spellcasting classes are still appealing to many players, because they present their own strengths.
To look at a few non-magical extraordinary abilities which compete with the supernatural abilities: many martial classes get Extra Attack. Rogues get Sneak Attack. Fighters get Action Surge and Second Wind. Battle Master fighters get Combat Manoeuvres. Barbarians get Rage. Monks get Flurry of Blows. The list goes on. Non-magic users still get lots of cool features, which at least partially balances the lack of spell-casting power.
I had a similar scenario in another campaign I ran, although it was World of Darkness with a homebrew magic system rather than D&D. In World of Darkness, the means to gain abilities (including at character creation) is to spend XP on getting Traits for your character. I had made my magic system part of this Traits system, such that a player needed to buy the Trait which let him be a spellcaster at character creation, then spend more XP on learning schools of magic and spells. However, they need to choose between spending XP on magic Traits, or on other Traits, liking having money, or having ranks in an organisation, or kung-fu skills, or being more hardy, or being a cool gunslinger. In essence, choosing to be a spellcaster represented an opportunity cost, sacrificing other advantages in exchange for having magic powers. Of the three players in that campaign, only one was a spellcaster. Another was a ninja, who had anti-magic Traits and kung-fu Traits. The third player specifically chose to play an ordinary person, and picked Traits which gave them money, status and contacts (social interactions being weighted more heavily in this system than D&D).
In your modern setting, you probably won't be using the base classes as-is, but you should draw inspiration from them. For each supernatural ability you grant a supernatural class or race, give a similarly cool extraordinary non-supernatural ability to the non-supernatural classes and races. You might have gunslingers who can pepper their enemies with bullets. You might have scientists who can pull knowledge from what seems to be thin air. You might have aristocrats who possess great wealth and powerful allies. You might have investigators who can shake off fear and spot even the faintest clues. You might have diplomats who can fast-talk their way past enemies and bolster allies with their words. You could give the non-supernatural races an additional Feat (as the Variant Human in 5e), or maybe some extra skill proficiencies, or perhaps some other benefit which makes sense in your setting.
Your player characters can still be awesome without magic powers, you just have to ensure that the non-magical player character options still present cool abilities.