I answered a similar (though not exact) question Thomas Jefferson's relationship with other slaves that may be of help. I'm going to use part of my answer from there, on here, since I talk about the frequency of sexual relationships between enslaved women and white men.

There was definitely a large number of enslaved women who had a sexual relationship with white men, most likely owners or relations of their owners. Often times this did result in the birth of children between the two. Historians have discussed this many times over the last century. Articles like this one actually show quite well how common sexual contact between white male owners and female enslaved women resulted in the birth of illegitimate children, stating, “Sexual abuse of slave women was extremely common, and the victims experienced no justice.”

One of the most earliest, and arguably most significant works about this type of abuse was the narrative account by a former slave named Jarriet Jacobs. Her account, entitled, Incidents in the Life of a Slave Girl was published in 1861, and was the first time that, in print, it accounted for how slave owners sexually abused those whom they enslaved. History would show that this account was far from uncommon, and historians showed, especially throughout the 1970s and 1980s (as original research heavily studied this field) that it was extremely common and that apparently everyone turned a blind eye to it.

The reasons that slave owners did this, apart from the sexual gratification, was to punish and assert control over enslaved women. (Women and Slavery - Boundless Open Textbook. Boundless U.S. History. 2015). But enslaved women also were not viewed as humans, but rather a commodity. As Jacobs recalled in her account, “women are considered of no value, unless they continuously increase their owner’s stock. They are put on a par with animals.”(page 49). This is significant because it then became common for male owners to try and get their slaves pregnant in order to sell the offspring later, if she wasn't already having sex with other enslaved men.

You asked if this was frowned upon, and in many ways, yes it was, at least publicly. We do know that it happened, and we have various accounts in letters between white men that they at times discussed it, but it wasn't something that people largely boasted about in public. As /u/Georgy_K_Zhukov pointed out in this this post, it was largely swept under the rug, where white society largely pretended it didn't happen.