Since you separate the two I suppose you don't think Matthew 15:18 applies here. I'll grant that for now for the sake of discussing another factor which intertwines them:
It certainly applies. The Greek verb in Matthew 15:11, 18, & 20 is κοινόω. The basic meaning of the whole word group κοιν- is "to be common." It is about sharing in community. Koinonia is an English word based on this Greek root meaning: "fellowship," "communion." What "defiles" (the way it is often translated in those verses) is acting just like "common" or "ordinary" people. God's people are to be "holy," which essentially means, "something 'set apart'," or "something different." That's what the Torah commands were meant to do: to distinguish God's people from the other peoples living around them.
Note: Non-Jews were not bound to the clean/unclean commands of the Torah. While everyone would have natural bodily discharges, and would need to deal with corpses, God's people had to follow a ritual afterwards to purify their uncleanness (commonness). Gentiles neither felt guilty nor ritually unclean by doing such things.
Jesus words, as I have interpreted them:
Throughout the Old Testament, God’s people were not to act like the people around them. They were to be different. So they didn’t work on the seventh day. They didn’t eat some foods. They didn’t worship the local gods and goddesses. They did some other things that might seem strange to the folks around them; but those differences are what made them special – the holy people of God – set apart from other people. They weren’t to be like the common or ordinary peoples in the area.
When Christians think and speak and act like everybody else, they become common and ordinary, which becomes defiled, contaminated, unclean – but certainly not beyond redemption by God.
Jesus indicates that such commonness begins from within, not from without. We will see that this woman’s "great faith" [the Canaanite woman in Matthew 15:21-28] comes from within. She had none of the outside trappings of piety or holiness – nothing that would set her apart from common pagans.
Israelites followed the rules about being unclean, so they didn't feel guilt about it. We don't follow the rules; something within that is tricky to put your finger on exactly may interpret the ignoring of the rules as a sin, and the resultant needless spread of the uncleanness as evidence of guilt. Then those sensitive enough to perceive it feel the "something" as an icky feeling.
Gentiles did not follow the rules about being unclean and they didn't feel guilty about it. It could be that these unclean rules came about because people felt "icky" about blood from a woman, semen from a man, touching dead bodies, etc. These are necessary things about which one should not feel guilty - even if they feel a bit "icky."
And wouldn't guilt flow more easily between two unclean persons, or from a clean to an unclean person (probably as the clean person shames the unclean person for some minutia)? The unnatural direction would be from an unclean person to a clean person, (who stays clean). Being clean & staying that way as much as possible helps to guard against others foisting their guilt on you.
Certainly. We have sayings, "one bad apple spoils the whole bunch" and "birds of a feather flock together."
When I worked at an alcoholic rehab hospital, clients were advised (even ordered) to get a new group of friends. If they continue socializing with their drinking buddies, they will bring them down. It even went so far that a friend's daughter in rehab for drug abuse was told that she had to leave her church youth group. She had to develop a new group of friends (mostly from the local NA group).
However, we are also told in the Old Testament, and what we see coming from Jesus, is that by touching or being touched by the holy thing, one becomes holy. Bread and wine touched by the holy Word of God becomes holy communion which touches our lives to make us holy.
Have you ever noticed that non-observant Jews of good character are way less spiritual or mystical-oriented than Christians? They are closer to atheists in their practice even if they still believe in God. The reason for this is that what they perceive as the Divine is unmanaged & treacherous. The quickest solution to this is to shut down the relationship rather completely because the ratio of curses to blessings is not going to be in their favor. So they don't even pray and are so rational they offend God or whatever it was that posed as God to them. In contrast, non-observant Christians of comparable good character are more likely to continue pursuing spiritual things, even if they don't attend church or confession, and even if they don't tithe. Their navigation of the spiritual surroundings is still riskier without a church community, but not as high-stakes as for non-practicing Jews. So they can maintain a relationship with God while not anticipating a deluge of bad things. (What I am getting at: Skepticism, for those who develop it, is equivalent to ghosting your relationships and otherwise trying to shut them down. It is a useful tactic if the relationship needs to end.)
That's true if one believes that the relationship depends on what we do. Jews, regardless of their religious observances, are still the chosen people of God. God said so. It's like a misbehaving children: the parents may not like what they are doing, but they continue to be their children.
The above paragraph explains how non-observant Jews handle the risk of guilt related to ignoring the rules. They are very cautious about abandoning their rational outlook; it keeps them safe. Yet moderate-to-liberal Christians are willing to open this massive can of worms just score a point in an argument over sexuality or some other topic. It doesn't seem right at all.
Many of my relatives and some good friends are non-observant Jews. I don't see them feeling guilt over ignoring the rules. We used to joke that one cousin could smell mom baking a ham from 200 miles away, and he'd show up for dinner. Another man said, "I like lobster." There is no guilt in disregarding Torah commands.
In terms of sexual sins and punishment, even orthodox Jews almost never follow Torah commands on this.
First of all, the Torah (Deuteronomy 17:6-7) requires at least two witnesses. They would have to see the adultery or a man lying with man as with a woman in order to bring charges against the person. Hearsay is not sufficient. Conjecture is not sufficient. There have been a couple of times I've spent the night at a female friend's house. We slept in separate rooms. When traveling in a Gospel team, I often slept in the same bed as another male team member. We did not break any commandments.
Secondly, those same verses require the witnesses to be the first ones to put the guilty to death. They would have to be the ones to cast the first stones.
If you want to follow the rules about sins, you must also be willing to follow the rules about punishments.