Thank you for raising the good issue. Maimonides (Hil’ Issurei Biah 13:14-16) explains that all of King Solomon’s wives converted before they were permitted to marry the king. The same was true of Samson before marrying Philistine women, and possibly of Ruth and Orpah before they married their Jewish husbands.

Even so, their conversions were considered questionable. Maimonides explains that it was plausible that Solomon’s wives converted not out of sincerity, but in order to marry into royalty. In fact, as the Book of Kings attests (I Kings 11:4-10), in Solomon’s old age some of his wives reverted to their idolatrous ways. The Torah further accuses King Solomon of going along with them. However, the Talmud (Shabbat 56b) explains that this was not so. The intent of the Torah was that Solomon was at fault for not properly rebuking his wives – which, considering his stature, was tantamount to his accepting idolatry himself.

Elsewhere the Talmud (Yevamot 76a) states that converts were not accepted at all in the times of Kings David and Solomon for the same reason as above. Since Israel was ascendant, the concern was too great that outsiders would want to convert in order to join the “winners” and not out of love for God and His Torah. (Needless to say, this has not been a concern throughout virtually all of Israel’s history.)