Look into the pick / pick branch setup, not the parallel setup. (Parallel is evil!)
It is a wee bit more complicated to use in modern experience (as is almost everything… vote for classic 
)
If you set up a pick activity, and within that activity 2 pick branch activities you are set.
As condition you do a element exists, one for each login button. As action the matching logon actions.
Your bot will validate both conditions (sort of parallel) and once a match is found it will follow that branch and ignore the rest. It is perfect for your use case. If you have more conditions such as an already logged in application, add a similar condition for an element specifically for a logged in page.
Note: if none of your conditions are met, it will select your 1st branch as a default.