Ask the question what would happen if "our price" is asked by the "big Prince" to sell up so that he can get Newcastle. If this is a feasibility, then that shows the level of conflict that is there. If this scenario is not possible and "our prince" could do what he likes then there is no conflict of interest. Another example would be could our government do a deal with a country for millions of pounds but that country didn't like a specific company or individual operating within its borders and insisted that that business leaves, as condition of any deal. Would our government as part of a huge trade deal say "forget the trade deal Johnny Used Cars must continue to sell his second hand shit to you". We are a democracy of sorts and would stop that company in an instant, for the greater good. This is the same conflict of interest that we are talking about with the house of Saud and they are feudal and not even a representative democracy.
I think in the end as usual the Premier league, FA and the Government will sign this deal through, they always take the money. Whether "our Prince" has to sell, or some other condition, it will go through and the fact that it is directly funded by a government (not an individual) that kills journalists in its own embassy, kills women and children and the Yemen and has horrific human rights abuses in its own country will not be considered.
My son is in a verbal fight with a Geordie fan on instagram. The Geordie wants the money but doesn't want to accept that direct money from the Saudi Government (again not an individual) used to whitewash their appalling human rights record does not implicate Newcastle in any way. If you take the money you are therefore complicit. I have to say I was not pleased we got the Prince but I would have to stop supporting us in any way and go and watch York City (my nearest other club) even though I'm lifelong a Blade and from Sheffield if we were funded by money put aside for Saudi PR purposes.