For one, I think we need to be careful how we interpret opinion/subjectivity.
In my view, economics is as much a methodology as a body of knowledge. Given a question about social behaviour, I can write down a set of assumptions that form an economic model and solve that model to answer the question. Whether the assumptions (be they standard or unorthodox) that are made are good or not is, of course, usually somewhat subjective. I do not think this subjectivity is itself a problem for out site.
The whole point of this mode of working is that the formalism of a model forces you to make your assumptions explicit so that your peers can judge the merits of your work accordingly. I think answers involving this kind of subjectivity should be welcome. That's not to say that a mathematical model should be a necessary for a good question/answer: often, purely non-technical statements also appeal to an economic logic that implies a model—even if the model itself is never written down.
What, I think, should not be welcome are answers predicated on a particular ideological position (i.e. purely normative arguments) or speculation the cannot obviously be grounded in a sound economic mechanism or empirical evidence.
Here's a (stylised for clarity) example of what I think is and is not okay:
Firstly, not okay because purely ideological/normative (not to mention dubious economic reasoning):
A monopoly manufacturer $M$ should not be allowed to merge with monopoly retailer $R$ because the owners of $M$ make enough money already.
Secondly (and a bit more subtly), this is not okay. Although this seems to be a less opinion based answer, the economic basis for the argument is not clear and so it is hard to judge whether there is any merit to this or whether it is pure speculation:
The monopoly manufacturer $M$ should not be allowed to merge with monopoly retailer $R$ because that will make the merged $MR$ very powerful, which is likely to be bad for consumers.
Thirdly, I think this (perhaps in a slightly more developed form) is okay:
Consider a monopoly manufacturer $M$ that sells its good via monopoly retailer $R$. Consumer demand for the final good is given as a decreasing function of the retail price $D(p)$, and the manufacturer's unit cost is $c$. The manufacturer sets a wholesale price, $p_M$, whilst the retailer sets the retail price $p$.
The retailer's profit is $D(p)(p-p_M)$, which is maximised when $D'(p)(p-p_M)+D(p)=0.$ The solution is the optimal retail price, $p^*$. The manufacturer's profit is $D(p^*)(p_M-c)$, which is maximised when $$D'(p^*)\frac{\partial p^*}{\partial p_M}(p_M-c)+D(p^*)=0.$$ In particular, we must have $p_M>c$.
If the two firms merge then the merged entity maximises profits with the standard first-order condition: $D'(p)(p-c)+D(p)=0.$ Since the unmerged $p_M$ is greater than $c$, it is immediate that the merged entity sets a lower price so that consumer surplus increases. Moreover, since the merged entity is now operating at the optimal price with respect to the entire market, its profits must have increased. The merger therefore yields a Pareto improvement. This line of reasoning is likely to lead regulators to look favourably on such mergers.
The important point here is that, even though some of the assumptions in the above might be quite stark and are clearly open to criticism (i.e. the legitimacy of this analysis is somewhat subjective), there is a clear and transparent economic analysis behind the statement. The same analysis could, in principle, be presented without any mathematics provided the economic mechanism is made clear enough. In any case, such an analysis might either stand alone or be paired with empirical evidence on the issue in question.
