The oil type in this recipe doesn’t sound appealing.

You can certainly change up the fat. It's mostly contributing lipids. There might be some variations in texture depending on what oil/fat you select.

You could even just use a different pie crust. It won't be the Hesser family peach tart anymore but would a French-style peach tart made with pâte brisée (full of butter) be inferior?

That's really your call.

What Gammy said! You can make it with any oil you like. I've even made it with canola oil so that there's no pronounced oil flavor.

Use whatever sounds good to you! I have made this as written with olive oil and it was delicious. I have made it with almond oil, too.