What safeguards did the LDS have back in the 19th century?
Many, the most important being that at that time and place, the practice had the Lord’s approval, divine sanction, and blessing. Okay, if you don’t believe that the LDS Church has (or had) any divine sanction for anything, that won’t mean a lot to you. But it means a lot to LDS people including me, who know that it does. There were other safeguards. Those who practised it were a very small percentage of LDS people (between 2% to 5%); and they had to be approved. I recall having read somewhere that those wanting to practice it had to obtain approval from the First Presidency, although I can’t find the source for it right now. They had to be approved for worthiness. I have searched the Internet, and found the following information. It is an extract from the interview of Gordon B. Hinckley by Larry King. Emphasis is mine:
Gordon B. Hinckley: When our people came west they permitted it on a
restricted scale.
Larry King: You could have a certain amount of…
Gordon B. Hinckley: The figures I have are from—between two percent and five percent of our people were involved in it. It was a very limited practice;
carefully safeguarded. In 1890, that practice was discontinued. The president of the church, the man who occupied the position which I occupy today, went before the people, said he had, oh, prayed about it, worked on it, and had received from the Lord a revelation that it was time to stop, to discontinue it then. That’s 118 years ago. It’s behind us.
Source.
Are they different from current polygamous sects?
Very much so, the most important being that they have no divine sanction for their practice, as the LDS Church did at that time.
If polygamy were legal why not allow it within the LDS?
If it were legalized, I can’t guess what the Church’s reaction to it would be. But I am of the opinion that the Church would oppose its legalization were the issue to come up, for the reasons previously described.
zerinus