my understanding is that qt5-network is compliant with openssl 1.0.2 and openssl 1.1 yet on openssl 1.1 I get  

/usr/local/bin/clang++50 -c -O2 -pipe -fstack-protector -fno-strict-aliasing -std=c++1z -fvisibility=hidden -fvisibility-inlines-hidden -fno-exceptions -Wall -W -Wdate-time -pthread -fPIC -DQT_OPENSSL -DQT_SSL -DQT_NO_USING_NAMESPACE -DQT_NO_FOREACH -DQT_USE_SYSTEM_PROXIES -DQT_NO_NARROWING_CONVERSIONS_IN_CONNECT -DQT_BUILD_NETWORK_LIB -DQT_BUILDING_QT -DQT_NO_CAST_TO_ASCII -DQT_ASCII_CAST_WARNINGS -DQT_MOC_COMPAT -DQT_USE_QSTRINGBUILDER -DQT_DEPRECATED_WARNINGS -DQT_DISABLE_DEPRECATED_BEFORE=0x050000 -DQT_NO_EXCEPTIONS -D_LARGEFILE64_SOURCE -D_LARGEFILE_SOURCE -DQT_NO_DEBUG -DQT_CORE_LIB -I. -Ikernel -I../../include -I../../include/QtNetwork -I../../include/QtNetwork/5.9.4 -I../../include/QtNetwork/5.9.4/QtNetwork -I/usr/local/include/qt5/QtCore/5.9.4 -I/usr/local/include/qt5/QtCore/5.9.4/QtCore -I/usr/local/include/qt5 -I/usr/local/include/qt5/QtCore -I.moc -I/usr/local/include -I/usr/local/lib/qt5/mkspecs/freebsd-clang -o .obj/qsslcertificate_openssl.o ssl/qsslcertificate_openssl.cpp
ssl/qsslcertificate_openssl.cpp:69:30: error: member access into incomplete type 'X509' (aka 'x509_st')
        return qHashBits(x509->sha1_hash, SHA_DIGEST_LENGTH, seed);
                             ^
/usr/local/include/openssl/ossl_typ.h:119:16: note: forward declaration of 'x509_st'
typedef struct x509_st X509;
               ^
ssl/qsslcertificate_openssl.cpp:93:68: error: member access into incomplete type 'X509' (aka 'x509_st')
            QByteArray::number(qlonglong(q_ASN1_INTEGER_get(d->x509->cert_info->version)) + 1);
                                                                   ^
/usr/local/include/openssl/ossl_typ.h:119:16: note: forward declaration of 'x509_st'
typedef struct x509_st X509;
               ^
ssl/qsslcertificate_openssl.cpp:102:45: error: member access into incomplete type 'X509' (aka 'x509_st')
        ASN1_INTEGER *serialNumber = d->x509->cert_info->serialNumber;
                                            ^
/usr/local/include/openssl/ossl_typ.h:119:16: note: forward declaration of 'x509_st'
typedef struct x509_st X509;
               ^
ssl/qsslcertificate_openssl.cpp:238:32: error: member access into incomplete type 'X509' (aka 'x509_st')
    X509_PUBKEY *xkey = d->x509->cert_info->key;
                               ^
/usr/local/include/openssl/ossl_typ.h:93:16: note: forward declaration of 'evp_pkey_st'
typedef struct evp_pkey_st EVP_PKEY;
               ^
ssl/qsslcertificate_openssl.cpp:251:36: error: member access into incomplete type 'EVP_PKEY' (aka 'evp_pkey_st')
    } else if (q_EVP_PKEY_type(pkey->type) == EVP_PKEY_EC) {
                                   ^
/usr/local/include/openssl/ossl_typ.h:93:16: note: forward declaration of 'evp_pkey_st'
typedef struct evp_pkey_st EVP_PKEY;
               ^
ssl/qsslcertificate_openssl.cpp:256:36: error: member access into incomplete type 'EVP_PKEY' (aka 'evp_pkey_st')
    } else if (q_EVP_PKEY_type(pkey->type) == EVP_PKEY_DH) {
                                   ^
/usr/local/include/openssl/ossl_typ.h:93:16: note: forward declaration of 'evp_pkey_st'
typedef struct evp_pkey_st EVP_PKEY;
               ^
8 errors generated.
*** [.obj/qsslcertificate_openssl.o] Error code 1

make[1]: stopped in /usr/ports/net/qt5-network/work/qtbase-opensource-src-5.9.4/src/network
1 error

make[1]: stopped in /usr/ports/net/qt5-network/work/qtbase-opensource-src-5.9.4/src/network
===> Compilation failed unexpectedly.
Try to set MAKE_JOBS_UNSAFE=yes and rebuild before reporting the failure to
the maintainer.
*** Error code 1

Stop.
make: stopped in /usr/ports/net/qt5-network

===>>> make build failed for net/qt5-network
===>>> Aborting update

===>>> Upgrade of qt5-core-5.9.4_1 to qt5-core-5.9.4_2 complete


===>>> You can restart from the point of failure with this command line:
       portmaster <flags> net/qt5-network 

This command has been saved to /tmp/portmasterfail.txt