No, and yes. You can start a brand new account on the first day of a league and be at par with everyone else. The vast majority of the game is accessible with no demands on you aside from time and skill. Every purchase you make is cosmetic only, simply changing the way some spells look or giving you a pet that follows you around and looks cool while doing nothing extra.
The one exception? Stash tabs. Tabs that specialize in holding certain items for you in your stash. Tabs that let you sell items to others with greater ease. It has gotten to the point where if you want to be best of the best, you should probably have the extra tabs. Why? Because at the endgame, you’ll need to start trading for items that make your build sing, or simply eke out the extra 15% damage that multiplies with other sources to make your dps soar into the millions, because PoE is all about finding something that you can push past where it was supposed to stop being good. Without those stash tabs, making cool items or easily trading with others is much more difficult.
Now, how much would it cost you to be ‘competitive’ with tabs? Probably $10 at most. For a game that I’ve played for over a decade and probably 1000-2000 hours at this point, I think the <$100 bucks I’ve thrown their way is worth it. I have friends who love the game and likely have 3k+ hours in it, and they’ve only spent $150 or so. I think that’s pretty reasonable for that much enjoyment.