I’ve written about this some in the past. If by “liberal” you mean what people ordinarily mean when they talk about “liberalism,” then no, you cannot be both a good Catholic and a good liberal. You can be a good one only to the extent you are a bad other.
At the heart of liberalism is the cult of the self-creating, self-defining, self-actualizing, utterly autonomous superman, liberated from all bonds of history, tradition, morality, law, etc. If you believe in this, then you are a liberal. You are also a bad Catholic. If you reject this as a Satanic delusion, then you are a bad liberal and (probably, though not necessarily) a good Catholic.
This is exactly the sort of thinking that gets people confused about these things.
The Church’s teachings acknowledge that there is some prudential leeway in deciding what sort of positions on certain issues to embrace. In some cases it may be permissible to choose a superficially leftist position. But since liberalism denies that these positions are prudential, even when you adopt them, you cannot adopt them for liberal reasons.
For instance, the Church has always and everywhere taught the moral liceity of the death penalty as a matter of principle. It currently states that the circumstances of the present age make it imprudent to execute people. That is a prudential, non-doctrinal, non-moral position with which people can in good faith disagree. You might accept that position. But there’s a massive gulf between “the death penalty is a bad idea right now” and “the death penalty is gravely evil,” the latter being a liberal position and flatly contrary to Church teachings.
Likewise with immigration. We do not get disregard the Church’s teachings of old re: the duties of immigrants toward their host nations, the rule of law, the common good, the rights of workers, etc., and so declare together with liberals that open borders are a matter of moral urgency. The best you can say is that it’s a good idea to have open borders (and I don’t know why you’d even think that given the state of the economy).