I do have some other angles on it to suggest.
Yes, opposite political opinions might undermine mutual respect, and be bad for your business or, more possible and worse, detract from the passion of your encounter. However, there is something else to consider here.
What is wrecking our political climate its parochial and incestuous nature. People are far too willing to retreat into their own faction and talk safely to others of their ideology, rather than anyone in disagreement with it. This isolation endangers us, because every ideology in humanity has its liars, opportunists, and psychopaths. The less a faction trusts all others, the more falsehoods are likely to circulate within that faction, unchecked against anything outside, and the more likely the liars, opportunists and psychopaths are to take control.
Now, disagreement is intellectual, but animosity and suspicion are emotions. If you disagree with a man politically, but you still satisfy him completely, you've most likely reduced that hostility, if only for a while. This is something that only a courtesan can do. It might make him more receptive and less judgmental of yours, or others.
Actually, courtesans are a banished political resource. Just by being in business unashamed, they could act as "cross-polinators" and reduce factionalization (strange as it is to refer to a female courtesan as a cross-polinator). They really need to get more politically interested, just from their self-interests, because this society's shameful treatment of you is due to wrongful political decisions made before any of us were born. These should be reversed, as they are connected intimately to most other political issues.
However, any political discussion fit into a two hour, sexually charged session is likely to be rushed. If you're talking about a 48 hour, then your client is wealthy, and more likely to have the political outlook of the wealthy.
I do have more to say about this... but I am now dead tired.
/Zin