I don’t know if thats true: I think everyone wants a “fair” distribution of wealth. The question is in the definition of fair, and means to achieve it. Conservatives believe that distribution achieved by tax and regulation will hurt the total economic production of the US, and lead to everyone being worse off, though more equal (in the extreme: everyone is equally poor), and they also consider it fair that the distribution is unequal (as do liberals). Its just a matter of how unequal.
But at least part of their definition of includes that they have the chance to increase their position, which is incompatible with tax/regulation at the extreme: if everyone has their incomes set in stone by the government, there is no chance to change in status.
But losing all low-level jobs to robots, notably, removes that chance. For different reasons than the liberal (who dislikes it for the centralization of wealth/power, and the extreme polarization of wealth distribution), conservatives would intuitively be against it for the denial of opportunity across the board
Tldr: everyone hates being poor/homeless, and too many people being homeless will cause a revolt regardless of their individual political leanings.
One aspect of UBI (when/if we can afford to implement it) is that it presents some solution the problem you describe if it's unconditional. If everyone has an set-in-stone income provided by the society because the robots are doing all the low-level jobs and the society doesn't need their labor, then they still have sufficient free time and ability to do something extra to increase their position.
There are many useful things that aren't (or won't be) viable as jobs because they pay too little or too sporadically to sustain yourself, however, they do provide enough to increase your revenue and status, and give a feeling of opportunity - if you'd have the basics provided in some other way.
One function of UBI has never been clear to me: if everyone has X, then no one does.
Applied to UBI’s case, the baseline of $0 has been “lifted” to say $1500; wouldn’t that just cause the market to increase prices proportionally, until $1500 is effectively the same as $0? Specifically, those baseline goods/services where that $1500 targets?
I would imagine luxury goods wouldn’t change much, as those spending in the area won’t change their spending behavior significantly with a fresh $1500; but a poorer community certainly would, and I would expect the market to match
In a modern first world economy (i.e. the only economy where UBI starts making some sense, and we're probably talking decades in the future so even more automation/productivity than now), the basket of goods that would be considered "basic" constitute something like <10% of total consumption and production. There would be some inflation caused by extra buying power, but it's not expected to be prohibitive in all the commoditized products such as food; I mean, the amount of consumed food would not change meaningfully as we feed pretty much everybody anyway, the only question is how the compensation is arranged - it doesn't matter that much for the economy if the poor unemployed person gets fed by food stamps, conditional social security, universal basic income, government supplied food packages, charity cash donations or charity soup kitchens.
One aspect that would change is the rental market. We would expect the landlords to try and capture much of that money. However, the big impact of UBI on rent is that it decouples the residental areas from the industrial areas; if you don't need to live where the jobs are and can credibly leave for a place where rents are cheaper, then some people will do so and that puts a limit on the rents.
As you state, small poor communities would feel a significant impact; however, in their case the main effect would be that they would become subsidized by the other parts of the society - much of the UBI they get would be spent on goods coming in from outside; their local market won't impact the price of a bottle of Coca Cola or a bag of potatoes, it's coming "from outside" anyway.
The cost of local services, on the other hand, would become much more spread out - if currently the cost for many services clusters around a single point (often close to minimum wage) because everybody needs a job so they do that service even if they don't want to; and everybody needs to eat, so they have to charge a reasonable amount even if they would be doing it as a hobby; In an UBI world you'd expect the cost of services to spread out widely so that services that are pleasant and interesting (for the provider) are cheaper than now, and services that suck for the workers become more expensive, as the workers now have a choice.
But at least part of their definition of includes that they have the chance to increase their position, which is incompatible with tax/regulation at the extreme: if everyone has their incomes set in stone by the government, there is no chance to change in status.
But losing all low-level jobs to robots, notably, removes that chance. For different reasons than the liberal (who dislikes it for the centralization of wealth/power, and the extreme polarization of wealth distribution), conservatives would intuitively be against it for the denial of opportunity across the board
Tldr: everyone hates being poor/homeless, and too many people being homeless will cause a revolt regardless of their individual political leanings.