Well, Amarr royal houses.
Ardishapur. Well, they mostly seem to be a very inward-focused house, so dealing with them as a godless foreigner might be difficult. Unless you have contacts with the Ammatar.
Kador. Uriam views himself as somewhat of a cosmopolitan. We know that he's been known to see personally at least Gallenteans (assumably young ladies, in his bedroom). And interestingly for a Kador, he is reformist. Not sure how much the personal attack on the Federation worked to hurt this. (Still a bit puzzled on the attack.)
Khanid. They will trade with outsiders, and have a plenty of non-Amarr employees in their corps. Expect to deal with a Deteis negotiator.
Kor-Azor. They are diplomatic, which does not imply pacifist. Doriam and the "new Aritcio" are known to be reformist. I'd say that someone of True Amarr blood might give an audience to outsiders (Aritcio himself had a Gallentean exchange student with him in an event organized in a cathedral - and no, I don't think it was a church service). Of course, if you make an ass out of yourself, you'll find yourself in the mines of Inis-Ilix.
Sarum. Formerly Amarrian supremacist. Merimeth Sarum is a complete question mark to me. I would expect them to continue being Amarr supremacist. Meeting with a True Amarr Holder? You better have very powerful weapons. For sale, that is.
Tash-Murkon. They trade. Davit's fortune got them the royal status, and Catiz is a self-made woman with her personal worth equal to her father's. And then she inherited Davit. I'd expect that some of the more liberal Holders might be willing to do business in person. Younger generation especially.
And then there is one more thing to think about, namely there's Holders and then there is Holders. I wouldn't expect to deal the same way with someone who's a Holder of a core system than with someone who is a Holder over a small station in some backwater world. A poor Holder might be more willing to make deals with foreigners if it is beneficial to them - for other Amarr, they can use their noble status for leverage, but for foreigners, this doesn't necessarily work.