Straw Man,
I would suggest that completely RAW you cannot maintain having your Cleric Domain granted powers and enter Ur-Priest at the same time.
I would direct you to Complete Divine pg. 70 the Ur-Priest Special requirements.
"The character must have no ability to cast divine spells. If such spellcasting ability was previously possessed (as with an ex-cleric), that ability is forever forsaken. The character must be trained by another ur-priest."
Please note that there are, in fact, 2 distinct requirements. We both don't care about the training from another Ur-Priest so forget that.
You are taking levels in Cleric. Obviously you do not worship a particular deity and follow your own ethical/philosophical code - granted on that part.
How then do you propose fulfilling the first requirement of Ur-Priest? Namely "The character must have no ability to cast divine spells."
I assume you are going to *choose* to "have no ability to cast divine spells" - but RAW I only see two ways for you to do that - having a Wisdom score of 9 or lower OR alternatively...the second sentence of Ur-Priest special requirements which in essence are the "ex-cleric" rules.
As I quoted above, Ur-Priest indicates that if you had previously possessed divine spellcasting ability you can forsake that ability forever AS WITH AN EX-CLERIC.
The "ex-cleric" rules PhB pg. 33 state that you lose your class features. Class features such as domains.
Therefore, to enter into Ur-Priest after being in a class that could cast divine spells, you must do so "as with an ex-cleric" and hence "as with the ex-cleric" rules you must lose your domains.
If you do not wish to be subject to the "ex-cleric" rules then, unless you have Wisdom of 9 or don't take levels in Cleric, I do not see how you can RAW fulfill "The character must have no ability to cast divine spells."
If you would like to point to a source that states you can lose your divine spellcasting ability at-will, then I would be convinced. Choosing not to prepare spells does not make you lose the ability to cast - otherwise a cleric who ran out of spells for the day could qualify - unless of course that's how you're reading "no ability to cast divine spells." Because no=zero, right? Besides that, you still have to qualify "as with an ex-cleric".
In fact, if you wanted to get even more RAW, the ONLY way you could enter Ur-Priest [having already possessed divine spellcasting ability] would be "as with an ex-cleric" i.e. you would have to worship a deity to qualify for the "ex-cleric" text. Let me restate this to be even clearer; being ineligible from the domain loss of the "ex-cleric" text 'because you don't worship a particular deity' would mean you are similarly ineligible from the required entry into Ur-Priest 'because you don't worship a particular deity'.
Strictly RAW you're probably already ineligible without a deity - but I'm sure no DM will hold that against you so long as you enter Ur-Priest "as an ex-cleric" - without the Domains.