It will probably only affect Patreon’s share of FOSS-projects starting today (and thus doesn't already have a Patreon).
Of course if enough people start using GitHub Sponsors, end-users may make it a expectation/demand to be able to sponsor their favourite projects there if they are going to bother (much like users today won’t bother to sign up for a Patreon-competitor).
And then it might start having a noticeable effect.
That said, anecdotally speaking, today only one of my Patreon pledges are for software projects, and most are for youtubers.
If that holds up for other people too, I suspect Patreon will be fine.