There are many examples of this. As someone stated in a comment, there are literally scores if not hundreds of denominations, just within Evangelical Protestantism. Plus many more if you include all the branches of mainline protestant churches. In many of these churches, the prohibition is in their doctrinal statement, and in others, it's not part of the statement of faith but strict church protocol or tradition which they say is based on principles.
Two examples I can think of that fit your description.
- alcohol in any form. This is not explicitly in the doctrinal statement but widely condemned, prohibited in Nazarene Churches, most Southern Baptist, Bible Methodist, Church of God Holiness and many Pentecostal churches.
2.Another example is that many churches have a custom of prohibiting anyone from taking communion who has not been baptized. No clear scriptural support of this, but they make the case based on baptism being an act of obedience in the New Testament and Communion an extension of this. This is a common practice in Baptist and Evangelical churches in Poland, Denmark and even some in the US.
Another example is that some churches only allow people to take communion who are members. This was the practice of a reformed PCA church I attended. It was very offensive to guests who couldn't take part in the Lord's supper. There are most often presented as individual church policies, which usually are determined at the local level. This is the case in many Evangelical Free Church of America churches, which is a denomination, but every local congregation is entirely autonomous and self led.
One of the biggest examples is the ban/ prohibition of musical instruments in the Church of Christ. Instruments are mentioned all through the scriptures, and there is no ban or prohibition anywhere against instruments. The reasoning is that there was no mention of NT churches using musical instruments - so it's an argument from silence.
You mentioned the example of self- baptism, but on the topic of baptism, many Protestant churches will prohibit a parent or friend from baptizing someone, or even the person who led him or her to Christ, and this is nowhere in scripture, but the reasoning is that this is the responsibility of an appointed elder or deacon, and that allowing a member to baptize is risky. This is common in Nazarene churches, some Pentecostal churches, some Baptist churches, and even some Evangelical churches. The church I currently attend is Baptist, and they only have staff pastors baptize. This was also the case in one Evangelical Free church, and also the case in a reformed church I attended.