How are the contrasting political ideas of the Federalists and Republicans still relevant ?
The contrasting political views of these parties or groups are still relevant to some degree because some of them still resonate with us today.
Not all of their beliefs are still important. No one, for example, really believes that the US could be nation of small farmers any more. Not many people at all would be interested in having a confederation rather than our federal system of government. Such views have become almost completely obsolete.
However, there are still aspects of their contrasting political views that are relevant to us today. For example, issues of the power of the federal government are still very important. There are major quarrels between those who would like to reduce federal power and those who feel that it is acceptable and beneficial. As another example, there are conflicts still between those who would like to run the country largely for the sake of the elites (in other words, people who believe that we need to cater to the needs of big business) and those who believe that we should hold to more populist views.
In short, the contrasting political views of these parties are still relevant today because some of the same issues continue to divide Americans.