Capitalizing pronouns (e.g. he, him, his, you, your, etc.) referring to the Blessed Trinity has not been a widespread practice in Christian tradition. In fact, these pronouns are never capitalized in the source documents. They are not capitalized in the Greek text of the Scriptures. Neither did St. Jerome capitalize them when he translated these texts into Latin Vulgate.
Even as the biblical texts were translated into English, the pronouns remained in the lower case. This is true of both Catholic and Protestant translation of the Bible. The Douay-Rheims Bible did not use them, neither did the King James. Neither do more than 30 current or old translations that I consulted online.
Outside the Scriptures, the English translation of the Catechism of the Council of Trent used lowercase pronouns, as does the current Catechism of the Catholic Church.
Thus we see the use of the lowercase for pronouns referring to the Divine Persons in biblical text.
Some years ago, at least in English-speaking countries, there was a pious practice of using the uppercase for pronouns referring to members of the Trinity. However, this practice was neither widespread nor ancient.
As for God’s name being holy, this is absolutely true. Thus, Father, Son and Holy Spirit are capitalized, as is the name of Jesus.
But pronouns are not proper names — they are, by definition, words that stand for or point back to proper nouns.
One may well argue that such pronouns should be capitalized, but given the widespread and ancient practice to the contrary, one ought be careful not to impugn motives of impiety for those who do not do so.