Many people don't support 100% of their party's policies - they just agree with them on the 2 or 3 things that are really important to them. This is a normal state of affairs in a two-party system.
For example, maybe I really like my party's stance on abortion and energy policy; I'm indifferent to their stances on farm subsidies, gun control, and immigration; and I feel their stances on trans rights and corruption could be improved a fair bit.
That would mean, when I meet someone from a different party, we could actually agree on a great many issues.
That's just... assuming you more-or-less support the planks/stances/actions of party you've just told them you consider yourself affiliated with. Where's the identity part come in?