Easier than the Flair-It type fittings are John Guest type fittings that seal by o-ring & metal grabbers. Sometimes called "stab" or "push" fittings, you press the square end cut of bare tubing into the fitting, encounter the o-ring's resistance, push harder & POP the fitting past the o-ring.
You can get versions of these in other brands at Home Depot & Lowes (H.D. brand in brass is "SharkBite"). You will be looking to cut off the existing Flair-it fitting to a clean square 1/2" o.d. PEX tubing end, then apply a new "push by xxx" fitting, where xxx matches to the gender & thread of your new faucet. The orange apron at H.D. or blue apron at brand L home improvement centers can help if you take in the old PEX pipe end & your new faucet (or use one of theirs for show & tell?). Should be either a straight or 90 degree single fitting that will adapt easily. At most 2 pieces per hot or cold end.
Baja-tested '08 2-slide 36'
Alpine: The Ultimate DIY'er Project