At the end of the day, these are questions that need to be asked in a specific situation to a rabbi who is familiar with the parties involved. Here however are some general guidelines that seem right to me.
I understand that there is often a lot of pressure at a wedding to find “roles” or “honors” for important friends and guests. Witnesses however play an important legal function and must be chosen with that function in mind.
According to halakha, “kosher” witnesses must be adult, male and not related to each other or to the bride and groom. They must also be religiously observant. Maimonides goes out of his way in his Code of Law to note that the reason we disqualify relatives is NOT that we fear they may be untrustworthy, but simply because that is what Scripture requires—it is, in other words, a requirement of law, not a comment on how we think different groups of people might behave. I believe that the same may be said of some of the other requirements of witnesses, including the requirement that they be male.
The problem with having Reform or Conservative witnesses at an Orthodox wedding is that since those movements do not understand Jewish law in the same way as the Orthodox community, and may not even consider it binding, they are probably outside the category of “religiously observant” for this purpose. Even Orthodox witnesses are often counseled to privately repent their sins before serving as witnesses, and an Orthodox witness who was known to be in public violation of one or more commandments might also be disqualified. Reform and Conservative guests or family members of the couple should understand that their own movements have taken their own principled positions on matters of Jewish practice which cannot always be reconciled with Orthodox understandings of halakhah—it is not, therefore, a personal slight if they not asked to serve in the capacity of witnesses, any more than it is when a Reform or Conservative rabbi is not asked to perform an Orthodox wedding.
Of course, many Jews attend Reform or Conservative synagogues without necessarily being convinced of those movements’ ideologies, but those are also often cases in which the individuals in question are not fully observant of Jewish law in other ways. At the very least, Orthodox rabbis usually require that the witnesses identify as Orthodox and are committed to Shabbat, Kashrut and other definitive religious practices. Not having kosher witnesses can sometimes allow a wedding to be considered invalid down the line, which is presumably not what somebody opting for an Orthodox wedding ceremony probably desires. Again, these are questions that should be addressed to the rabbi on the scene.
Looking at things from the other direction, I would generally discourage Orthodox Jews from serving as witnesses at non-Orthodox weddings. Standing as witness is a technical religious act and it implies buying into and supporting the legal standing of the entire process, which in my opinion is difficult for an Orthodox Jew to do. While I would certainly attend and celebrate the wedding of a non-Orthodox friend or relative, I would hesitate to take a formal role in the ceremony. There is also a certain degree of reciprocity in not taking a role at someone else’s wedding that I would not be comfortable having them fulfill in my own.
Finally, there is one more possible concern which is rather more sensitive. Many marriages today end in divorce. It is not uncommon for couples who were not strongly committed to halakha in the first place to seek a civil but not a religious divorce and to remarry without ever having dissolved their first marriages according to halakha. Such cases can be very painful because the children of a second marriage in which the first was never dissolved can be prohibited by Torah law from marrying into the Jewish community. One of the ways rabbis avoid this problem is by finding ways to show that the first marriage in such a case was not really valid, often by showing that the witnesses were not observant. But this might become harder if the witnesses do in fact meet the requirements of Jewish law.
Weddings often serve as opportunities for a couple to celebrate their friendships, their relatives and the things that are important to them. This is as it should be. With respect to the choice of witnesses however, there simply is less leeway than in many other matters. For an Orthodox person or a person who has chosen to hold an Orthodox wedding ceremony, this is one area in which the integrity of Jewish law and commitment to its traditions ought to be paramount, which is why these matters should be discussed with the rabbi of their choice.