Some changes in https://github.com/golang/go/issues/29162#issuecomment-445888885

main.go

package main

import (
	"bufio"
	"bytes"
	"compress/gzip"
	"crypto/tls"
	"fmt"
	"io"
	"io/ioutil"
	"log"
	"net"
	"net/http"
	"net/http/httptest"
	"net/textproto"
	"strings"
	"time"
)

func main() {
	getResponseWithCustomClient()
	getWithDefaultClient()
}

func healthCheckHandler(w http.ResponseWriter, r *http.Request) {
	w.Header().Set("Content-Type", "application/json")
	encoding := r.Header.Get("Accept-Encoding")
	if strings.Contains(encoding, "gzip") {
		encoder, _ := gzip.NewWriterLevel(w, 6)
		encodingName := "gzip"

		w.Header().Set("Transfer-Encoding", encodingName )
		w.Header().Set("Accept-Encoding", encodingName)
		w.Header().Add("Vary", "Accept-Encoding")
		fmt.Fprint(encoder, `{"alive": true, "query": "`+r.URL.RawQuery+`"}`)
	} else {
		fmt.Fprint(w, `{"alive": true, "query": "`+r.URL.RawQuery+`"}`)
	}
}

// Test to check if the server will exit gracefully when client exits
func getWithDefaultClient() {
	handler := http.HandlerFunc(healthCheckHandler)
	server := httptest.NewServer(handler)
	defer server.Close()

	serverURL := server.URL + "?test=true"
	req, err := http.NewRequest("GET", serverURL, nil)
	if err != nil {
		log.Println("http request error", err.Error())
		return
	}
	req.Header.Set("Accept-Encoding", "gzip")

	res, err := http.DefaultClient.Do(req)
	if err != nil && !strings.Contains(err.Error(), "context canceled") {
		log.Println("http client error", err.Error())
		return
	}
	contents, err := ioutil.ReadAll(res.Body)
	fmt.Println("response", string(contents))
}

func getResponseWithCustomClient() {
	handler := http.HandlerFunc(healthCheckHandler)
	server := httptest.NewServer(handler)
	defer server.Close()

	serverURL := server.URL + "?test=true"
	req, err := http.NewRequest("GET", serverURL, nil)
	if err != nil {
		log.Println("http request error", err.Error())
		return
	}
	req.Header.Set("Accept-Encoding", "gzip")

	netClient := &http.Client{
		Timeout:   time.Second * 10,
		Transport: &transferEncodingRedactor{base: http.DefaultTransport.(*http.Transport)},
	}
	res, err := netClient.Do(req)
	if err != nil && !strings.Contains(err.Error(), "context canceled") {
		log.Println("http client error", err.Error())
		return
	}
	contents, err := ioutil.ReadAll(res.Body)
	fmt.Println("response", string(contents))
}

type transferEncodingRedactor struct {
	base *http.Transport
}

func (rt *transferEncodingRedactor) RoundTrip(req *http.Request) (*http.Response, error) {
	// Optimistic route i.e common case.
	res, err := rt.base.RoundTrip(req)
	if err == nil || res != nil {
		return res, err
	}

	// An error occured here but now time ot examine the contents
	if !strings.Contains(err.Error(), "unsupported transfer encoding") {
		return res, err
	}

	u := req.URL
	var conn net.Conn
	switch req.URL.Scheme {
	case "https":
		tr := rt.base
		if tr == nil {
			tr = http.DefaultTransport.(*http.Transport)
		}
		host := req.URL.Host
		if !strings.Contains(host, ":") {
			host += ":443"
		}
		conn, err = tls.Dial("tcp", host, tr.TLSClientConfig)
	default:
		host := req.URL.Host
		if !strings.Contains(host, ":") {
			host += ":80"
		}
		conn, err = net.Dial("tcp", host)
	}

	if err != nil {
		return nil, fmt.Errorf("dial error: %v", err)
	}

	// Ensure we close the connection after.
	// Perhaps you might want to reuse it per host?
	defer conn.Close()

	s := u.Path
	if q := u.RawQuery; len(q) > 0 {
		s += "?" + q
	}

	intro := fmt.Sprintf("%s /%s HTTP/1.1\r\nHost:%s\r\n\r\n", req.Method, s, u.Host)
	fmt.Fprint(conn, intro)

	br := bufio.NewReader(conn)
	// And now we've got the case of an unsupported transfer
	// encoding time for a raw fetch and header rewrite.
	tp := textproto.NewReader(br)

	protoLine, err := tp.ReadLine()
	if err != nil {
		return nil, fmt.Errorf("ReadLine error: %v", err)
	}
	// Time to parse the headers
	rhdr, err := tp.ReadMIMEHeader()
	if err != nil {
		return nil, fmt.Errorf("ReadMIMEHeader: %v", err)
	}
	hdr := http.Header(rhdr)
	// Now rewrite the header
	if te := hdr.Get("Transfer-Encoding"); te == "gzip" {
		hdr.Set("Content-Encoding", "gzip")
		delete(hdr, "Transfer-Encoding")
	}

	// After this rewrite, reassemble the already read parts back
	// and then get them to ReadResponse
	hdrBuf := new(bytes.Buffer)
	if err := hdr.Write(hdrBuf); err != nil {
		return nil, fmt.Errorf("Rewriting header to wire: %v", err)
	}

	reconstructed := io.MultiReader(strings.NewReader(protoLine+"\r\n"), hdrBuf, strings.NewReader("\r\n"), br)
	return http.ReadResponse(bufio.NewReader(reconstructed), req)
}

Response

response {"alive": true, "query": "test=true"}
2019/07/03 15:03:13 http client error Get http://127.0.0.1:51639?test=true: net/http: HTTP/1.x transport connection broken: unsupported transfer encoding "gzip"