How can Christian approach to counseling differ from a more secular approach regarding certain issues (abortion, homosexuality, sexual purity) and given that counselors should not impose their values on clients, how should Christian therapists deal with theological issues that arise in counseling?
Clearly, a Christian approach to counseling is going to be more strongly centered around Christian values and morals than a secular approach will be. Christians are going to feel much more strongly that there are rights and wrongs associated with sexual purity, homosexuality, and other such things than secular counselors are. This means that Christian counselors may be much more conflicted when presented with clients who have issues in these areas.
It is not clear to me that all counselors believe that they should refrain from imposing their values on their clients. In two of the links below, we see very strong rejections of the idea that Christian counselors should help clients accept and live with homosexuality. These articles clearly show that there are Christian counselors who are willing to impose their values on their clients.
If a Christian counselor is faced with issues like the ones you identify, and if they do not want to impose their values on the client, they have two main options. First, the counselor can simply decline to treat the client and can refer them to a different counselor who will be able to treat them. Second, the counselor can try to help the client without endorsing their point of view. This counselor could try to help the client uncover their feelings about certain issues and to determine what is making the client unhappy. The counselor could help the client think through the issues. By doing these things, the counselor could help the client make his or her own decisions. The counselor would be helping the client to think more clearly, but they would not be telling the client what to do. In this way, a Christian counselor could help a client without trying to impose Christian values on that client.