How can two biological sequences be anything but homologous?
Homology in this context is always a matter of degree exactly because of shared ancestry. Measures of homology are often in terms of "percent homology" (or more often "percent similarity" as evidence of homology) or some other measure that allows representation of that degree.

To emphasize why this makes sense, think about a receptor family. In an extant organism, you might have 3 receptors that all are homologous. However, if receptors 2 and 3 are more similar to each other than to receptor 1, then you can make some better assumptions about the history of the evolution of receptors 1 to 3, that there is likely a "common ancestor receptor" to both 2 and 3. There is more "information" if you consider the degree of homology rather than just its existence.

At some extremes, sequences could be so different that even if they share a lineage they may have now diverged to the point that they are not distinguishable from independent sequences. However, selective pressures prevent such complete reorganization in key sequences and so at least some homology can be maintained across very distantly related organisms.

As far as deciding what is "homologous" versus "not homologous", that is somewhat of an arbitrary threshold that depends on levels of evidence and the purpose for recognizing the homology.