Does equality of economic opportunity support or conflict with social welfare policies for those in poverty
You will find great difference of opinion, usually depending on one's opinion of Social Welfare programs.
One school of opinion is that Social welfare programs are "entitlements" provided by the Government. People from this school of thought tend to think that equality of economic opportunity conflicts with Social Welfare. Entitlements take away incentive to work, so people are more likely to pass up opportunities in favor of the entitlement. They will typically point to entitlements paying more than typical blue collar compensation. While this may be true, what if this is the market is saying that the compensation needs to be higher?
The other school of opinion is that Social Welfare Programs are "Safety nets." People from this school tend to think that equality of economic opportunity supports social welfare policies. Welfare is just a cushion for those who miss an opportunity, so that they will be ready to seize the next opportunity to come along. Supporters may point out that if you come to job opportunity looking like a tramp, you are less likely to get the job than a less qualified applicant dressed like a businessman. But will you pass up an opportunity because it looks like a "dead-end part-time"?
I'm in the "safety net" school of thought. I do believe that Social welfare keeps the less fortunate afloat, so they can seize the opportunities that present themselves. I believe that this actually levels the playing field allowing the best qualified candidate to look presentable and thus prove they are the best qualified.