I think it would be useful to configure minimal lifetime support along with minimum pledge. For example, I sell my game on itoch.io for $15. Also, I have two $5 patrons. One of them supports me for 6 months, and his lifetime support is 5x6 = $30. It's fair to give him access to my itch.io. The other patron supports me for only one month, and his lifetime support is 5x1 = $5. This patron should wait.
Viewing post in Patreon integration on itch.io comments
If I may, I do not see where you should have any concerns. The price of your game here is higher than the Patreon paid you, so therefore they will only have access to see your game here, not play it for free, unless you make it free. This is just another way to broaden the base you reach. So many here do not know to check for Patreon and vice versus. I think it will be a win-win for you.
Just my opinion. I do not work for either of these two.
Good luck on your game