At the current state of the game, even with Goblin or Exalted reputation the recipe will be around 1080 gold to purchase thus @ F2P you are capped @ 1000 gold. If the cost was 1250 gold you could get it at 1000 gold @ Exalted.
You do get access to weekly Shadowlands Dungeon quests for reputation so technically one can get to Exalted with the Court of Harvesters after a few months of these weekly quests as well as if able to pick them as your Covenant you can get some reputation with other quests but its slow-go.
Some do strict F2P for the challenge and that's perfectly fine and understandable.
However, if you want to play F2P long-term without the constraint of being "pure" F2P, it is absolutely worth paying $15 for a month. There should be a list of everything you can and should do to improve your F2P experience in a month. Some initial thoughts:
- Get to max level (70 currently without buying TWW)
- Do the DF campaign to unlock adventure mode
- Do the BFA intro so you can skip on alts
- Do the SL campaign so you can skip on alts and buy Renown catch ups
- Do the Legion campaign so you can skip on alts and boost an alt's rep with rep tokens
- Buy a stockpile of gems and enchants rather than levelling the professions
- Unlock allied races and, optionally, heritage armor
- Get Exalted with MoP reps and buy the Grand Commendations
- Get max DF Renowns
- ON ALT: get Revered Rustbolt and buy the Extraordinary Augment recipe. It costs (IIRC) ~1700g so you can't buy it F2P