My Rav told me that one cannot be oiver on Bain Adam L’chaveiro because of a chumra of Bain Adam l’Makom.
The example he gave was that if a guest came to your house and brought you a cake or a bottle of wine with a hechsher that you would normally not eat, (not because it’s treif ch”v, but because you are machmir on a better hechsher – I think the example he gave was a wine with the OU only) you have a chiyuv bain adam lichaveiro to serve it and use it. And that overrides your “minhag” of only using badatz.
Now with regard to your dishwasher, (I would ask my Rav first, but I think he would tell me) that the dishwasher was (probably) cleaned well before your first use and there is no treif in it now, so whatever chumrah I would have would be innapropiate at your home.
(Disclosure: I have not learned well bassar b’chalav – so I don’t know what the practical issues of the machlokes with regard to dishwashers is and if its a question of chumra to wait a year or if its a shaila of real tarfus)